First passages in bounded domains: When is the mean first passage time meaningful?

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(ω) distribution of the random variable ω=τ1/(τ1+τ2), which is a measure for how similar the first passage times τ1 and τ2 are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(ω) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(ω), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.

Entire functions uniformly bounded on balls of a Banach space

Let X be an in�finite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B1 � X and unbounded on another given ball B2 � X have been obtained. In this paper we consider the problem of �finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection. RESUMEN. Sea X un espacio de Banach complejo de dimensión infinita. En este trabajo, los autores estudian el problema de encontrar una función entera en X que esté uniformemente acotada en una colección de de bolas en X y que no esté acotada en las bolas de otra colección.

Unconformity-bounded stratigraphic units (UBSUs) in an italian alluvial-plain area: recognizing and dating

We studied the coastal zone of the Tavoliere di Puglia plain, (Puglia region, southern Italy) with the aim to recognize the main unconformities, and therefore, the unconformity-bounded stratigraphic units (UBSUs; Salvador 1987, 1994) forming its Quaternary sedimentary fill. Recognizing unconformities is particularly problematic in an alluvial plain, due to the difficulties in distinguishing the unconformities that bound the UBSUs. So far, the recognition of UBSUs in buried successions has been made mostly by using seismic profiles. Instead, in our case, the unavailability of the latter has prompted us to address the problem by developing a methodological protocol consisting of the following steps: I) geological survey in the field; II) draft of a preliminary geological setting based on the field-survey results; III) dating of 102 samples coming from a large number of boreholes and some outcropping sections by means of the amino acid racemization (AAR) method applied to ostracod shells and 14C dating, filtering of the ages and the selection of valid ages; IV) correction of the preliminary geological setting in the light of the numerical ages; definition of the final geological setting with UBSUs; identification of a ‘‘hypothetical’’ or ‘‘attributed time range’’ (HTR or ATR) for each UBSU, the former very wide and subject to a subsequent modification, the latter definitive; V) cross-checking between the numerical ages and/or other characteristics of the sedimentary bodies and/or the sea-level curves (with their effects on the sedimentary processes) in order to restrict also the hypothetical time ranges in the attributed time ranges. The successful application of AAR geochronology to ostracod shells relies on the fact that the ability of ostracods to colonize almost all environments constitutes a tool for correlation, and also allow the inclusion in the same unit of coeval sediments that differ lithologically and paleoenvironmentally. The treatment of the numerical ages obtained using the AAR method required special attention. The first filtering step was made by the laboratory (rejection criteria a and b). Then, the second filtering step was made by testing in the field the remaining ages. Among these, in fact, we never compared an age with a single preceding and/or following age; instead, we identified homogeneous groups of numerical ages consistent with their reciprocal stratigraphic position. This operation led to the rejection of further numerical ages that deviate erratically from a larger, homogeneous age population which fits well with its stratigraphic position (rejection criterion c). After all of the filtering steps, the valid ages that remained were used for the subdivision of the sedimentary sequences into UBSUs together with the lithological and paleoenvironmental criteria. The numerical ages allowed us, in the first instance, to recognize all of the age gaps between two consecutive samples. Next, we identified the level, in the sedimentary thickness that is between these two samples, that may represent the most suitable UBSU boundary based on its lithology and/or the paleoenvironment. The recognized units are: I) Coppa Nevigata sands (NEA), HTR: MIS 20–14, ATR: MIS 17–16; II) Argille subappennine (ASP), HTR: MIS 15–11, ATR: MIS 15–13; III) Coppa Nevigata synthem (NVI), HTR: MIS 13–8, ATR: MIS 12–11; IV) Sabbie di Torre Quarto (STQ), HTR: MIS 13–9.1, ATR: MIS 11; V) Amendola subsynthem (MLM1), HTR: MIS 12–10, ATR: MIS 11; VI) Undifferentiated continental unit (UCI), HTR: MIS 11–6.2, ATR: MIS 9.3–7.1; VII) Foggia synthem (TGF), ATR: MIS 6; VIII) Masseria Finamondo synthem (TPF), ATR: Upper Pleistocene; IX) Carapelle and Cervaro streams synthem (RPL), subdivided into: IXa) Incoronata subsynthem (RPL1), HTR: MIS 6–3; ATR: MIS 5–3; IXb) Marane La Pidocchiosa–Castello subsynthem (RPL3), ATR: Holocene; X) Masseria Inacquata synthem (NAQ), ATR: Holocene. The possibility of recognizing and dating Quaternary units in an alluvial plain to the scale of a marine isotope stage constitutes a clear step forward compared with similar studies regarding other alluvial-plain areas, where Quaternary units were dated almost exclusively using their stratigraphic position. As a result, they were generically associated with a geological sub-epoch. Instead, our method allowed a higher detail in the timing of the sedimentary processes: for example, MIS 11 and MIS 5.5 deposits have been recognized and characterized for the first time in the study area, highlighting their importance as phases of sedimentation.

Bounded non-deterministic planning for multimedia adaptation

This paper proposes a novel combination of artificial intelligence planning and other techniques for improving decision-making in the context of multi-step multimedia content adaptation. In particular, it describes a method that allows decision-making (selecting the adaptation to perform) in situations where third-party pluggable multimedia conversion modules are involved and the multimedia adaptation planner does not know their exact adaptation capabilities. In this approach, the multimedia adaptation planner module is only responsible for a part of the required decisions; the pluggable modules make additional decisions based on different criteria. We demonstrate that partial decision-making is not only attainable, but also introduces advantages with respect to a system in which these conversion modules are not capable of providing additional decisions. This means that transferring decisions from the multi-step multimedia adaptation planner to the pluggable conversion modules increases the flexibility of the adaptation. Moreover, by allowing conversion modules to be only partially described, the range of problems that these modules can address increases, while significantly decreasing both the description length of the adaptation capabilities and the planning decision time. Finally, we specify the conditions under which knowing the partial adaptation capabilities of a set of conversion modules will be enough to compute a proper adaptation plan.