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Stochastic Bundles, New Classes of Gaussian Processes and White Noise-space Analysis Indexed by Measures
Get PDFStarting from a fixed measure space (X,F,μ), with μ a positive sigma-finite measure defined on the sigma-algebra F, we continue here our study of a generalization W(μ) of Brownian motion, and introduce a corresponding white-noise process. In detail, the generalized Brownian motion is a centered Gaussian process W(μ), indexed by the elements A in F of finite μ measure, and with covariance function μ(A ∩ B). The purpose of our present paper is to make precise and study the corresponding whitenoise process, i.e., a point-wise process which is indexed by X, and which arises as a generalizedμderivative of W(μ). A key tool in our definition and analysis of this pair is a construction of three operators between the underlying Hilbert spaces. One of these operators is a stochastic integral, the second is a gradient associated with the measure μ, and the third is a mathematical expectation in the underlying probability space.We show that, with the setting of families of processes indexed by sets of measures μ, our results lead to new stochastic bundles. They serve in turn to extend the tool set for stochastic calculus
Identifying Common Patterns in the Time of Day of Mindfulness Meditation Associated with Long-Term Maintenance
Get PDFForming a habit of practicing mindfulness meditation around the same time of day is one strategy that may support long-term maintenance and in turn improve physical and mental health. The purpose of this study was to identify common patterns in the time of day of meditation associated with long-term meditation app use to assess the importance of temporal consistency for maintaining meditation over time. App usage data were collected from a random sample of 15,000 users who had paid for an annual membership to a commercial meditation app in 2017. We constructed three measures of temporal consistency in the time of day of meditation sessions in order to categorize users into one of three behavioral phenotypes: Consistent, Inconsistent, or Indeterminate. Panel data models were used to compare temporal consistency across the three phenotypes. Of the 4205 users (28.0%) in the final analytic sample, 1659 (39.5%) users were Consistent, 2326 (55.3%) were Inconsistent, and 220 users (5.23%) were Indeterminate. Panel models confirmed that temporal consistency had contrasting relationships with meditation maintenance among these three phenotypes (p \u3c 0.01). These findings revealed that temporal consistency was associated with meditation maintenance for less than half of app users, which suggests that other behavioral mechanisms in addition to temporally consistent habits can support meditation app use over time. This has important implications for researchers and policymakers trying to promote the maintenance of meditation and other complex health behaviors, such as increased physical activity and healthier diets
The Problem with “More is Better”: An Assessment of the “New” Contract Grading
Get PDFIn this article I discuss some of the issues that scholars are and aren’t writing about in relation to the recent resurgence in contract grading, and reflect on my own experience using contract grading in composition and other classes. I come to the topic as a scholar and university teacher in rhetoric and composition, though my discussion certainly is relevant to teachers in many disciplines and institution types. My aim is to offer an analysis of the benefits and drawback of the “new” contract grading, with special attention to what I call the “more is better” mantra that informs many current iterations of contract grading
Artificially Intelligent Maxwell\u27s Demon for Optimal Control of Open Quantum Systems
Get PDFFeedback control of open quantum systems is of fundamental importance for practical applications in various contexts, ranging from quantum computation to quantum error correction and quantum metrology. Its use in the context of thermodynamics further enables the study of the interplay between information and energy. However, deriving optimal feedback control strategies is highly challenging, as it involves the optimal control of open quantum systems, the stochastic nature of quantum measurement, and the inclusion of policies that maximize a long-term time- and trajectory-averaged goal. In this work, we employ a reinforcement learning approach to automate and capture the role of a quantum Maxwell\u27s demon: the agent takes the literal role of discovering optimal feedback control strategies in qubit-based systems that maximize a trade-off between measurement-powered cooling and measurement efficiency. Considering weak or projective quantum measurements, we explore different regimes based on the ordering between the thermalization, the measurement, and the unitary feedback timescales, finding different and highly non-intuitive, yet interpretable, strategies. In the thermalization-dominated regime, we find strategies with elaborate finite-time thermalization protocols conditioned on measurement outcomes. In the measurement-dominated regime, we find that optimal strategies involve adaptively measuring different qubit observables reflecting the acquired information, and repeating multiple weak measurements until the quantum state is \u27sufficiently pure\u27, leading to random walks in state space. Finally, we study the case when all timescales are comparable, finding new feedback control strategies that considerably outperform more intuitive ones. We discuss a two-qubit example where we explore the role of entanglement and conclude discussing the scaling of our results to quantum many-body systems
Contests with Ambiguous Prizes
No full textThis paper examines behavior in contests where the prize value is ambiguous. We develop a theoretical model of bidding in a Tullock contest with an ambiguous prize where contestants account for the ambiguity attitude of their rival. Ambiguity affects optimal behavior via two countervailing channels - a direct effect arising from contestants’ ambiguity about the value of the prize and an indirect effect corresponding to the effect of ambiguity on the opponent’s behavior. Using a controlled laboratory experiment, we elicit individual risk and ambiguity attitudes and compare predicted and observed behavior in contests with an ambiguous prize, a risky prize and certain prizes. A comparison between contests with ambiguous and risky prizes, shows that participants invest significantly less under ambiguity. Additionally, we decompose the effect of changing from a certain prize to an ambiguous prize into two components - the first is the effect of introducing risk and the second is the effect of introducing ambiguity. Empirically, we find that both effects are significant, but work in opposite directions
Design and Synthesis of a Novel Neuroprotective Brain-Targeting Amylin Receptor Antagonist
No full textAmylin receptor antagonist AC253 is a 24-amino acid peptide that provides neuroprotection against amyloid beta (Aβ)-induced cell death and toxicity. Additionally, AC253 has been shown to improve spatial memory in mouse models of Alzheimer’s disease (AD). Screening of short overlapping fragments (12-mer) of AC253 showed that N-terminal residues were responsible for high affinity binding to the amylin receptor (AMY3). Both AC253 and R5 (a 12-mer fragment) have a short half-life in human serum and are hydrophilic peptides with a low log P (-1.2 for AC253) and are not optimized for brain uptake. From the structure-activity relationship studies, we have designed a 16-mer analog (R16) from the N-terminal region of AC253 as a novel AmyR antagonist for better activity and blood-brain permeability. The goal of this study is to design and synthesize a novel neuroprotective analog of AC253 called R16 for enhanced blood-brain barrier targeting. R16 was synthesized using solid-phase peptide synthesis, purified and characterized by MALDI-TOF mass spectrometry and reversed-phase HPLC. The proteolytic stability of R16 was evaluated in human and mouse sera to determine the half-lives and proteolytically labile sites. The half-life of R16 was found to be 8.98 hours and 0.47 hours in human and mouse serum, respectively. The N-terminal of R16 was found to be accessible to proteolytic cleavage by serum proteases. Therefore, blocking N-terminal of R16 with a blood brain targeting peptide Angiopep-2 led to the design of a proteolytic stable blood-brain barrier targeting analog of R16, namely Angiopep2- R16 conjugate. The conjugate was synthesized, purified and characterized using reversed-phase HPLC and mass spectrometry, and was found to be \u3e95% pure. The conjugate will be further studied in the future to test its pharmacokinetics, stability, and brain activity