Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity

2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10.

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.

A kvázi- és általánosított hiperbolikus diszkontálás hosszú távon (Quasi- and Generalized Hyperbolic Discounting in Long Term)

Az intertemporális döntések fontos szerepet játszanak a közgazdasági modellezésben, és azt írják le, hogy milyen átváltást alkalmazunk két különböző időpont között. A közgazdasági modellezésben az exponenciális diszkontálás a legelterjedtebb, annak ellenére, hogy az empirikus vizsgálatok alapján gyenge a magyarázó ereje. A gazdaságpszichológiában elterjedt általánosított hiperbolikus diszkontálás viszont nagyon nehezen alkalmazható közgazdasági modellezési célra. Így tudott gyorsan elterjedni a kvázi-hiperbolikus diszkontálási modell, amelyik úgy ragadja meg a főbb pszichológiai jelenségeket, hogy kezelhető marad a modellezés során. A cikkben azt állítjuk, hogy hibás az a megközelítés, hogy hosszú távú döntések esetén, főleg sorozatok esetén helyettesíthető a két hiperbolikus diszkontálás egymással. Így a hosszú távú kérdéseknél érdemes felülvizsgálni a kvázi-hiperbolikus diszkontálással kapott eredményeket, ha azok az általánosított hiperbolikus diszkontálási modellel való helyettesíthetőséget feltételezték. ____ Intertemporal choice is one of the crucial questions in economic modeling and it describes decisions which require trade-offs among outcomes occurring in different points in time. In economic modeling the exponential discounting is the most well known, however it has weak validity in empirical studies. Although according to psychologists generalized hyperbolic discounting has the strongest descriptive validity it is very complex and hard to use in economic models. In response to this challenge quasi-hyperbolic discounting was proposed. It has the most important properties of generalized hyperbolic discounting while tractability remains in analytical modeling. Therefore it is common to substitute generalized hyperbolic discounting with quasi-hyperbolic discounting. This paper argues that the substitution of these two models leads to different conclusions in long term decisions especially in the case of series; hence all the models that use quasi-hyperbolic discounting for long term decisions should be revised if they states that generalized hyperbolic discounting model would have the same conclusion.

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.

Electronic Channels of Distributions: Challenges and Solutions for Hotel Operators

This paper addresses the issues of hotel operators identifying effective means of allocating rooms through various electronic channels of distribution. Relying upon the theory of coercive isomorphism, a think tank was constructed to identify and define electronic channels of distribution currently being utilized in the hotel industry. Through two full-day focus groups consisting of key hotel electives and industry practitioners, distribution channels wen identified as were challenges and solutions associated with each

Genetically Altered Foods: A Policy Issue for Multi-unit Food Service Operators

Although it is a substantial issue, the technology behind genetically altered foods and the concerns being raised about them are not well understood by most people. The authors discuss how genetically altered foods might fit into the business strategies of multi-unit food service operators as well as current policies and predispositions of multi-unit food service companies toward the use of genetically altered foods. They also outline the issues surrounding genetically altered food as they relate to the food service industry and provide a picture of where multi-unit food service operators currently stand on the technology

Electronic Channels of Distribution: Challenges and Solutions for Hotel Operators

This paper addresses the issues of hotel operators identifying effective means of allocating rooms through various electronic channels of distribution. Relying upon the theory of coercive isomorphism, a think tank was constructed to identify and define electronic channels of distribution currently being utilized in the hotel industry. Through two full-day focus groups consisting of key hotel executives and industry practitioners, distribution channels were identified as were challenges and solutions associated with each.

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.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

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.

Spectrally isometric elementary operators

We present criteria for unital elementary operators (of small length) on unital semisimple Banach algebras to be spectral isometries. The surjective ones among them turn out to be algebra automorphisms.