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Numerical solution of a PDE arising from prediction with expert advice
No full textThis work investigates the online machine learning problem of prediction with expert advice in an adversarial setting through numerical analysis of, and experiments with, a related partial differential equation. The problem is a repeated two-person game involving decision-making at each step informed by n experts in an adversarial environment. The continuum limit of this game over a large number of steps is a degenerate elliptic equation whose solution encodes the optimal strategies for both players. We develop numerical methods for approximating the solution of this equation in relatively high dimensions (n ≤ 10) by exploiting symmetries in the equation and the solution to drastically reduce the size of the computational domain. Based on our numerical results we make a number of conjectures about the optimality of various adversarial strategies, in particular about the non-optimality of the COMB strategy
LOCAL HALANAY’S INEQUALITY WITH APPLICATION TO FEEDBACK STABILIZATION
No full textWe provide a local version of an approach to proving asymptotic stability that is based on Halanay’s inequality. Our results are applicable to a family of nonlinear systems that contain state and input delays. We determine input-to-state stability inequalities when the systems contain additive uncertainty. We combine the results with an observer and a Gramian approach, to solve an output feedback stabilization problem. Our numerical examples illustrate how our theorems lead to new basin of attraction estimates
Nets of Standard Subspaces on Non-compactly Causal Symmetric Spaces
No full textLet G be a connected simple linear Lie group and H⊂G a symmetric subgroup such that the corresponding symmetric space G∕H is non-compactly causal. We show that any irreducible unitary representation of G leads naturally to a net of standard subspaces on G∕H that is isotone, covariant and has the Reeh–Schlieder and the Bisognano–Wichmann property. We also show that this result extends to the universal covering group of SL2(ℝ), which has some interesting application to intersections of standard subspaces associated to representations of such groups. For this, a detailed study of hyperfunction and distribution vectors is needed. In particular, we show that every H-finite hyperfunction vector is in fact a distribution vector
Realization of unitary representations of the Lorentz group on de Sitter space
Get PDFThis paper builds on our previous work in which we showed that, for all connected semisimple linear Lie groups G acting on a non-compactly causal symmetric space M=G/H, every irreducible unitary representation of G can be realized by boundary value maps of holomorphic extensions in distributional sections of a vector bundle over M. In the present paper we discuss this procedure for the connected Lorentz group G=SO1,d(R)e acting on de Sitter space M=dSd. We show in particular that the previously constructed nets of real subspaces satisfy the locality condition. Following ideas of Bros and Moschella from the 1990’s, we show that the matrix-valued spherical function that corresponds to our extension process extends analytically to a large domain Gℂcut in the complexified group Gℂ=SO1,d(ℂ), which for d=1 specializes to the complex cut plane ℂ∖(−∞,0]. A number of special situations is discussed specifically: (a) The case d=1, which closely corresponds to standard subspaces in Hilbert spaces, (b) the case of scalar-valued functions, which for d\u3e2 is the case of spherical representations, for which we also describe the jump singularities of the holomorphic extensions on the cut in de Sitter space, (c) the case d=3, where we obtain rather explicit formulas for the matrix-valued spherical functions
ROLE AND ELECTROPHYSIOLOGICAL PROPERTIES OF SEXUALLY DIMORPHIC OXYTOCIN RECEPTOR EXPRESSING NEURONS IN THE ANTEROVENTRAL PERIVENTRICULAR NUCLEUS OF THE FEMALE MICE
Get PDFOxytocin is a neurohypophyseal hormone that plays a crucial role in regulating mother-infant bonding and maternal behavior. Oxytocin modulates sex-specific parental behaviors by binding to the oxytocin receptor (OXTR)-expressing neurons in the brain. This study investigates the sexually dimorphic OXTR neurons in the anteroventral periventricular nucleus (AVPV) to understand how oxytocin modulates behavior in females. Specifically, we explored the behavioral roles, neural projections, and intrinsic electrophysiological characteristics of these neurons in the female mice. Using immunohistochemistry revealed that the number of OXTR-expressing neurons was enhanced in postpartum females compared with virgin females, suggesting that these neurons are involved in female-specific behavior, such as maternal behavior. Moreover, our study showed that a subset of the OXTR neurons in the AVPV are immunoreactive to tyrosine hydroxylase (TH+), an enzyme essential for dopamine synthesis. Therefore, this subset of OXTR-expressing neurons is likely dopaminergic, and their function may drive maternal motivation. In postpartum females, using DREADD coupled to the inhibitory G-protein (Gi), inactivated AVPV-OXTR neurons. This neuronal inactivation impaired maternal behavior, specifically pup retrieval and building nest. Since behavior is a direct result of neuronal activity, we extend our study further to characterize AVPV-OXTR neurons. Whole-cell patch clamp recordings revealed heterogeneity in the electrophysiological properties of AVPV-OXTR neurons. TH+ OXTR neurons displayed a pacemaker-like intrinsic rhythmic short bursting activity, whereas TH- OXTR neurons displayed either no firing at all, irregular firing, or a phasic firing. Moreover, some TH- OXTR neurons could switch back and forth among these firing patterns. The differences in the firing patterns between these two populations were likely derived from the difference in their expression of spike afterpotentials. TH+ OXTR neurons showed more depolarizing afterpotential (DAP) than after-hyperpolarization (AHP), while TH- OXTR neurons exhibited more AHP than DAP. Results from immunohistochemistry of patched neurons revealed TH- OXTR neurons showing more dendritic arborization than TH+ neurons. Altogether, this study will contribute to an enhanced understanding of oxytocin related neuronal mechanisms underlying sex-specific parenting behavior, potentially paving the way for developing new therapeutic approaches for sex-specific psychiatric disorders such as postpartum depression (PPD)
For Us, By Us: A Digital Ethnographic Exploration of Black Podcasts, Intimacy, & Sexual Pleasure
No full textSociological literature written about Black folks interprets their sexual behavior as unhealthy, risky, and non-normative. Black people are seldom acknowledged as humans, so it is not surprising to discover a discourse that does not portray them as sexual subjects. Studies examining Black sexual subjectivity through white and colorblind ideologies dominate the discussion, reproducing racist discourse historically ascribed to Black bodies. Guided by Audre Lorde’s concept of erotic as power, I document an alternative epistemology about Black sexuality. I argue the construction of Black sexuality must focus on sexual selfhood to grasp how this population conceptualizes and makes sense of their sexuality while navigating a sexually oppressive and repressive culture dominated by white standards. In a review of prominent literature surrounding Black sexuality, previous sociological approaches have failed to define Black sexuality beyond Eurocentric perceptions. Recognizing the agentive and authentic expression of Black identity in online spaces, this study examines how Black podcasters are shifting narratives repressing Black erotic freedoms. Two main themes are identified: unlearning through self scrutiny and negotiating pleasure in relationships. This work expands sociological imaginations of Black sexuality, pleasure, and understandings of digital practice among marginalized groups
A Machine Learning Approach to Cave and Sinkhole Prediction in the Cradle of Humankind: Implications for Fossil Prospecting in Paleoanthropology
No full textIn paleoanthropology, fossils are key to understanding hominin evolutionary relationships and paleoenvironments. Surveying an area for new fossil sites, however, is a labor-intensive and resource-draining activity. Machine learning prediction models trained on remotely sensed landscape imagery can be employed to alleviate difficulties associated with traditional survey practices by identifying areas of interest for fossil prospecting. The purpose of this dissertation is to compare and apply different machine learning frameworks that predict the location of cave entrances and sinkholes as a proxy for fossil sites in the Cradle of Humankind, South Africa. Machine learning models were trained using geomorphological landscape characteristics derived from multispectral satellite images, Digital Elevation Models (DEMs), and geologic maps in association with known cave and sinkhole localities in the region, in order to identify other areas with a similar suite of characteristics for survey.
This dissertation is divided into three main studies. The first utilizes a spatial 10-fold cross-validation method to evaluate Random Forest (RF) model efficacy on test datasets withheld from model training. The RF performed with an average 81.6% accuracy and an Area Under the Curve (AUC) score of 0.912. Variable permutation importance found that fault proximity, location within the Chuniespoort geologic Group, dolomite presence, chert presence, and elevation exhibited the highest importances for model accuracy. The second study compares five different machine learning frameworks for Cradle site prediction: RF, Support Vector Machine (SVM), Maximum Entropy (MaxEnt), 1D Convolutional Neural Network (CNN-1D), and 2D Convolutional Neural Network (CNN-2D). The CNN-1D outclasses the other models in average accuracy, recall, and F1 score but is prone to false positives. Conversely, MaxEnt’s high precision and low recall indicates it is cautious and prone to false negatives. The third study applies the CNN-1D and MaxEnt model in an ensemble approach to specific areas in and around the Cradle for ground-truthing surveys. Sixty-nine cave and sinkhole sites were recorded within or close to the boundaries of model survey zones across approximately 184 hectares. These results demonstrate the models’ ability to efficiently and successfully identify areas of interest for survey, which could greatly expedite future paleoanthropological prospecting efforts
The observability inequalities for heat equations with potentials
No full textThis paper is mainly concerned with the observability inequalities for heat equations with time-dependent Lipschitz potentials. The observability inequality for heat equations asserts that the total energy of a solution is bounded above by the energy localized in a subdomain with an observability constant. For a bounded measurable potential V = V (x, t), the factor in the observability constant arising from the Carleman estimate is best known to be exp(C||V||2/3) (even for time-independent potentials). In this paper, we show that, for Lipschtiz potentials, this factor can be replaced by exp(C(||V||1/2 + ||tV ||1/3)), which improves the previous bound exp(C|| V ||2/3) in some typical scenarios. As a consequence, with such a Lipschitz potential, we obtain a quantitative regular control in a null controllability problem. In addition, for the one-dimensional heat equation with some time-independent bounded measurable potential V = V (x), we obtain the observability inequality with optimal constant on arbitrary measurable subsets of positive measure both in space and time
Interval spectrum for electric quantum walk and related skew-shift CMV matrices
Get PDFWe show that for a family of quantum walk models with electric fields, the spectrum is the unit circle for any irrational field. The result also holds for the associated CMV matrices defined by skew-shifts, as well as a family of the Blattner and Browne model. Generalizations to CMV matrices with skew-shifts on higher dimensional torus are also obtained