A Characterization of Weakly Lindelöf Determined Banach Spaces

2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Weakly Compact Generating and Shrinking Markusevic Bases

2000 Mathematics Subject Classification: 46B30, 46B03.

Weakly-constrained codes for suppression of patterning effects in digital communications

We propose weakly-constrained stream and block codes with tunable pattern-dependent statistics and demonstrate that the block code capacity at large block sizes is close to the the prediction obtained from a simple Markov model published earlier. We demonstrate the feasibility of the code by presenting original encoding and decoding algorithms with a complexity log-linear in the block size and with modest table memory requirements. We also show that when such codes are used for mitigation of patterning effects in optical fibre communications, a gain of about 0.5dB is possible under realistic conditions, at the expense of small redundancy 10%). © 2006 IEEE.

An automated method for the determination of electroreception thresholds in weakly electric fish

Weakly electric fish produce a dual function electric signal that makes them ideal models for the study of sensory computation and signal evolution. This signal, the electric organ discharge (EOD), is used for communication and navigation. In some families of gymnotiform electric fish, the EOD is a dynamic signal that increases in amplitude during social interactions. Amplitude increase could facilitate communication by increasing the likelihood of being sensed by others or by impressing prospective mates or rivals. Conversely, by increasing its signal amplitude a fish might increase its sensitivity to objects by lowering its electrolocation detection threshold. To determine how EOD modulations elicited in the social context affect electrolocation, I developed an automated and fast method for measuring electroreception thresholds using a classical conditioning paradigm. This method employs a moving shelter tube, which these fish occupy at rest during the day, paired with an electrical stimulus. A custom built and programmed robotic system presents the electrical stimulus to the fish, slides the shelter tube requiring them to follow, and records video of their movements. I trained the electric fish of the genus Sternopygus was trained to respond to a resistive stimulus on this apparatus in 2 days. The motion detection algorithm correctly identifies the responses 91% of the time, with a false positive rate of only 4%. This system allows for a large number of trials, decreasing the amount of time needed to determine behavioral electroreception thresholds. This novel method enables the evaluation the evolutionary interplay between two conflicting sensory forces, social communication and navigation.

Waveform Detection of Conspecifics in the Weakly Electric Fish Gymnotus Carapo

Weakly electric fish use electric fields for communication and location of objects. Electroreceptors that are located around the mouth and along the length of the body are used in order to "decode" the electric organ discharge (EOD). The knollenorgan in Mormyriformes aids in distinguishing between different EODs. Gymnotiformes, however, have no such electroreceptors. How then are Gyrnnotiformes distinguishing between conspecific EODs? In this study scan sampling was investigated to determine whether Gymnotus carapo uses this mechanism to differentiate between distinct EODs. After determining whether Gymnotus carapo was discriminating between neighbor and stranger EODs, these same EODs were played to the test fish either jittered (the EOD of the test fish and that of the playback could not coincide) or non-jittered (the two EODs could coincide). The results show that the test fish was not discriminating between neighbor and stranger EODs. Thus, conclusions about the use of scan sampling by Gymnotus carapo to distinguish between EODs cannot be made.

A Method for Testing Object Localization as a Function of Eod Amplitude in the Weakly Electric Fish Brachyhypopomus Pinnicaudatus

I would like to thank Dr. Philip Stoddard for his patience and guidance throughout the past four years. He has not only taught me about behavior and electricity, but he has also taught me how to think scientifically. Vielka Salazar for making herself available to answer my questions and to help me with my projects. Montserrat Alfaro for providing me with support under times of frustration. Fabian A. Pal, who has often made himself available when I needed help to finish my projects, for being supportive, and for believing in me and my abilities. Most importantly, I would like to thank my parents who have shown tremendous support and patience during the past years. I would also like to thank the Honors Committee, specially Dr. Richards for taking the time to review my thesis and helping me modify it. Finally, I would like to thank the MARC program for providing me with financial assistance and the opportunity to perform this project.

Plasticity varies with boldness in a weakly-electric fish

The expression of animal personality is indicated by patterns of consistency in  individual behaviour. Often, the differences exhibited between individuals are consistent across situations. However, between some situations, this can be biased by variable levels of individual plasticity. The interaction between individual plasticity and animal personality can be illustrated by examining situation-sensitive personality traits such as boldness (i.e. risk-taking and exploration tendency). For the weakly electric fish Gnathonemus petersii, light condition is a major factor influencing behaviour. Adapted to navigate in low-light conditions, this species chooses to be more active in dark environments where risk from visual predators is lower. However, G. petersii also exhibit individual differences in their degree of behavioural change from light to dark. The present study, therefore, aims to  examine if an increase of motivation to explore in the safety of the dark, not only affects mean levels of boldness, but also the variation between individuals, as a result of differences  in individual plasticity.  Results: Boldness was consistent between a novel-object and a novel-environment situation in bright light. However, no consistency in boldness was noted between a bright (risky) and a  dark (safe) novel environment. Furthermore, there was a negative association between boldness and the degree of change across novel environments, with shier individuals  exhibiting greater behavioural plasticity.  Conclusions: This study highlights that individual plasticity can vary with personality. In  addition, the effect of light suggests that variation in boldness is situation specific. Finally,  there appears to be a trade-off between personality and individual plasticity with shy but  plastic individuals minimizing costs when perceiving risk and bold but stable individuals  consistently maximizing rewards, which can be maladaptive.

Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion

Recently, Bès, Martin, and Sanders [11] provided examples of disjoint hypercyclic operators which fail to satisfy the Disjoint Hypercyclicity Criterion. However, their operators also fail to be disjoint weakly mixing. We show that every separable, infinite dimensional Banach space admits operators T1,T2,…,TN with N⩾2 which are disjoint weakly mixing, and still fail to satisfy the Disjoint Hypercyclicity Criterion, answering a question posed in [11]. Moreover, we provide examples of disjoint hypercyclic operators T1, T2 whose corresponding set of disjoint hypercyclic vectors is nowhere dense, answering another question posed in [11]. In fact, we explicitly describe their set of disjoint hypercyclic vectors. Those same disjoint hypercyclic operators fail to be disjoint topologically transitive. Lastly, we create examples of two families of d-hypercyclic operators which fail to have any d-hypercyclic vectors in common.

Universality of weakly bound dimers and Efimov trimers close to Li-Cs Feshbach resonances

We study the interspecies scattering properties of ultracold Li-Cs mixtures in their two energetically lowest spin channels in the magnetic field range between 800 and 1000 G. Close to two broad Feshbach resonances (FR) we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of their binding energy on the external magnetic field strength. Based on the binding energies and complementary atom loss spectroscopy of three other Li-Cs s-wave FRs we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channels calculation. We extract the Li-Cs interspecies scattering length as a function of the external field and obtain almost a ten-fold improvement in the precision of the values for the pole positions and widths of the s-wave FRs as compared to our previous work (Pires et al 2014 Phys. Rev. Lett. 112 250404). We discuss implications on the Efimov scenario and the universal geometric scaling for LiCsCs trimers.

Unraveling the performance of dispersion-corrected functionals for the accurate description of weakly bound natural polyphenols

Long-range non-covalent interactions play a key role in the chemistry of natural polyphenols. We have previously proposed a description of supramolecular polyphenol complexes by the B3P86 density functional coupled with some corrections for dispersion. We couple here the B3P86 functional with the D3 correction for dispersion, assessing systematically the accuracy of the new B3P86-D3 model using for that the well-known S66, HB23, NCCE31, and S12L datasets for non-covalent interactions. Furthermore, the association energies of these complexes were carefully compared to those obtained by other dispersion-corrected functionals, such as B(3)LYP-D3, BP86-D3 or B3P86-NL. Finally, this set of models were also applied to a database composed of seven non-covalent polyphenol complexes of the most interest.

Weakly-constrained codes for suppression of patterning effects in digital communications

We propose weakly-constrained stream and block codes with tunable pattern-dependent statistics and demonstrate that the block code capacity at large block sizes is close to the the prediction obtained from a simple Markov model published earlier. We demonstrate the feasibility of the code by presenting original encoding and decoding algorithms with a complexity log-linear in the block size and with modest table memory requirements. We also show that when such codes are used for mitigation of patterning effects in optical fibre communications, a gain of about 0.5dB is possible under realistic conditions, at the expense of small redundancy (≈10%). © 2010 IEEE