BU Open Access Articles
https://hdl.handle.net/2144/16844
2019-04-24T03:37:48ZThe promise and pitfalls of differences-in-differences: reflections on '16 and Pregnant' and other applications
https://hdl.handle.net/2144/34895
The promise and pitfalls of differences-in-differences: reflections on '16 and Pregnant' and other applications
Kahn-Lang, Ariella; Lang, Kevin
We use the exchange between Kearney/Levine and Jaeger/Joyce/Kaestner on `16 and Pregnant' to reexamine the use of DiD as a response to the failure of nature to properly design an experiment for us. We argue that 1) any DiD paper should address why the original levels of the experimental and control groups differed, and why this would not impact trends, 2) the parallel trends argument requires a justification of the chosen functional form and that the use of the interaction coefficients in probit and logit may be justified in some cases, and 3) parallel trends in the period prior to treatment is suggestive of counterfactual parallel trends, but parallel pre-trends is neither necessary nor sufficient for the parallel counterfactual trends condition to hold. Importantly, the purely statistical approach uses pretesting and thus generates the wrong standard errors. Moreover, we underline the dangers of implicitly or explicitly accepting the null hypothesis when failing to reject the absence of a differential pre-trend.
2019-04-02T00:00:00ZRigorous justification of Taylor dispersion via center manifolds and hypocoercivity
https://hdl.handle.net/2144/34894
Rigorous justification of Taylor dispersion via center manifolds and hypocoercivity
Beck, Margaret; Wayne, Clarence Eugene; Chaudhary, Osman
Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to 1/ν, which is much faster than what would be produced by the static fluid if its viscosity is 0<ν≪1. This phenomenon is analyzed rigorously using the linear PDE governing the evolution of the solute. It is shown that the solution can be split into two pieces, an approximate solution and a remainder term. The approximate solution is governed by an infinite-dimensional system of ODEs that possesses a finite-dimensional center manifold, on which the dynamics correspond to diffusion at a rate proportional to 1/ν. The remainder term is shown to decay at a rate that is much faster than the leading order behavior of the approximate solution. This is proven using a spectral decomposition in Fourier space and a hypocoercive estimate to control the intermediate Fourier modes.
2018-01-01T00:00:00ZLocalized radial roll patterns in higher space dimensions
https://hdl.handle.net/2144/34892
Localized radial roll patterns in higher space dimensions
Bramburger, Jason J.; Altschuler, Dylan J.; Avery, Chloe I.; Sangsawang, Tharathep; Beck, Margaret; Carter, Paul; Sandstede, Bjorn
Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the length of the spatial interval over which these patterns resemble a periodic profile stays either bounded, in which case branches form closed bounded curves (“isolas”), or the length increases to infinity so that branches are unbounded in function space (“snaking”). In two space dimensions, numerical computations show that branches of localized rolls exhibit a more complicated structure in which both isolas and snaking occur. In this paper, we analyse the structure of branches of localized radial roll solutions in dimension 1+ε, with 0 < ε 1, through a perturbation analysis. Our analysis sheds light on some of the features visible in the planar case.
2018-01-01T00:00:00ZNonlinear stability of source defects in oscillatory media
https://hdl.handle.net/2144/34891
Nonlinear stability of source defects in oscillatory media
Beck, Margaret; Nguyen, Toan; Sandstede, Bjorn; Zumbrun, Kevin
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects are important as organizing centers of more complicated flows. Our analysis uses spatial dynamics combined with an instantaneous phase-tracking technique to obtain detailed pointwise estimates describing perturbations to lowest order as a phase-shift radiating outward at a linear rate plus a pair of localized approximately Gaussian excitations along the phase-shift boundaries; we show that in the wake of these outgoing waves the perturbed solution converges time-exponentially to a space-time translate of the original source pattern.
2018-02-21T00:00:00ZEquivalences and counterexamples between several definitions of the uniform large deviations principle
https://hdl.handle.net/2144/34888
Equivalences and counterexamples between several definitions of the uniform large deviations principle
Salins, Michael
This paper explores the equivalences between four definitions of uniform large deviations principles and uniform Laplace principles found in the literature. Counterexamples are presented to illustrate the differences between these definitions and specific conditions are described under which these definitions are equivalent to each other. A fifth definition called the equicontinuous uniform Laplace principle (EULP) is proposed and proven to be equivalent to Freidlin and Wentzell's definition of a uniform large deviations principle. Sufficient conditions that imply a measurable function of infinite dimensional Wiener process satisfies an EULP using the variational methods of Budhiraja, Dupuis and Maroulas are presented. This theory is applied to prove that a family of Hilbert space valued stochastic equations exposed to multiplicative noise satisfy a uniform large deviations principle that is uniform over all initial conditions in bounded subsets of the Hilbert space. This is an improvement over previous weak convergence methods which can only prove uniformity over compact sets.
2018-09-18T00:00:00ZUniform large deviation principles for Banach space valued stochastic differential equations
https://hdl.handle.net/2144/34887
Uniform large deviation principles for Banach space valued stochastic differential equations
Budhiraja, Amarjit; Dupuis, Paul; Salins, Michael
We prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDE) that is uniform with respect to initial conditions in bounded subsets of the Banach space. A key step in the proof is showing that a uniform large deviation principle over compact sets is implied by a uniform over compact sets Laplace principle. Because bounded subsets of infinite dimensional Banach spaces are in general not relatively compact in the norm topology, we embed the Banach space into its double dual and utilize the weak-$\star $ compactness of closed bounded sets in the double dual space. We prove that a modified version of our stochastic differential equation satisfies a uniform Laplace principle over weak-$\star $ compact sets and consequently a uniform over bounded sets large deviation principle. We then transfer this result back to the original equation using a contraction principle. The main motivation for this uniform LDP is to generalize results of Freidlin and Wentzell concerning the behavior of finite dimensional SDEs. Here we apply the uniform LDP to study the asymptotics of exit times from bounded sets of Banach space valued small noise SDE, including reaction diffusion equations with multiplicative noise and $2$-dimensional stochastic Navier-Stokes equations with multiplicative noise.
2018-03-05T00:00:00ZLarge deviations and averaging for systems of slow–fast reaction–diffusion equations
https://hdl.handle.net/2144/34886
Large deviations and averaging for systems of slow–fast reaction–diffusion equations
Hu, Wenqing; Salins, Michael; Spiliopoulos, Konstantinos
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is based on the weak convergence method in infinite dimensions, which results in studying averaging for controlled SRDEs. By appropriate choice of the parameters, the fast process and the associated control that arises from the weak convergence method decouple from each other. We show that in this decoupling case one can use the weak convergence method to characterize the limiting process via a "viable pair" that captures the limiting controlled dynamics and the effective invariant measure simultaneously. The characterization of the limit of the controlled slow-fast processes in terms of viable pair enables us to obtain a variational representation of the large deviation action functional. Due to the infinite--dimensional nature of our set--up, the proof of tightness as well as the analysis of the limit process and in particular the proof of the large deviations lower bound is considerably more delicate here than in the finite--dimensional situation. Smoothness properties of optimal controls in infinite dimensions (a necessary step for the large deviations lower bound) need to be established. We emphasize that many issues that are present in the infinite dimensional case, are completely absent in finite dimensions.
2017-10-07T00:00:00ZLocal Calabi–Yau manifolds of type A˜ via SYZ mirror symmetry
https://hdl.handle.net/2144/34881
Local Calabi–Yau manifolds of type A˜ via SYZ mirror symmetry
Lau, Siu; Kanazawa, Atsushi
We carry out the SYZ program for the local Calabi–Yau manifolds of type A˜ by developing an equivariant SYZ theory for the toric Calabi–Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov–Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood–Iqbal–Vafa (Hollowood et al., 2008).
2019-05-01T00:00:00ZOn the Chinese character 根 (Root)
https://hdl.handle.net/2144/34879
On the Chinese character 根 (Root)
Huang, Weijia; Tan, Yunfei
2019-01-01T00:00:00ZThe Serenity of West Point 寂静的西点军校
https://hdl.handle.net/2144/34878
The Serenity of West Point 寂静的西点军校
Huang, Weijia
Han, Xiaohui
2018-01-01T00:00:00ZThe Final days of working with Kwang-Chih Chang 和张光直先生工作的最后日子
https://hdl.handle.net/2144/34877
The Final days of working with Kwang-Chih Chang 和张光直先生工作的最后日子
Huang, Weijia
2002-01-01T00:00:00ZThe Church 教堂
https://hdl.handle.net/2144/34876
The Church 教堂
Huang, Weijia
2011-04-18T00:00:00ZAt the Harvard-Yenching Library Book Sale 哈佛燕京“卖”书记
https://hdl.handle.net/2144/34875
At the Harvard-Yenching Library Book Sale 哈佛燕京“卖”书记
Huang, Weijia
2011-11-24T00:00:00ZSupplement to "The sorted effects method: discovering heterogeneous effects beyond their averages"
https://hdl.handle.net/2144/34410
Supplement to "The sorted effects method: discovering heterogeneous effects beyond their averages"
Chernozhukov, Victor; Fernandez-Val, Ivan; Luo, Ye
This zip file contains the replication files for the manuscript. It also contains an online appendix. The supplementary material contains 7 appendices with additional results and some omitted proofs. Appendix C introduces some notation. Appendix D includes a brief review of differential geometry. Appendix E gathers the proofs of the key mathematical results in Appendix A. Appendix F provides sufficient conditions for the u-Donsker properties in Section 4. Appendix G extends the theoretical analysis to include discrete covariates. Appendices H and I report the results of 3 numerical simulations and an empirical application to the effect of race on mortgage denials, respectively.
Accepted manuscript full text available here: https://hdl.handle.net/2144/34409
2018-11-01T00:00:00ZFrontal and posterior subtypes of neuropsychological deficit in Parkinson's disease
https://hdl.handle.net/2144/34398
Frontal and posterior subtypes of neuropsychological deficit in Parkinson's disease
Miller, I. N.; Neargarder, Sandy; Risi, M. M.; Cronin–Golomb, Alice
Mild cognitive impairment in Parkinson's disease (PD) is heterogeneous in regard to affected domains. Although patterns of cognitive performance that may predict later dementia are as yet undetermined, posterior-versus frontal-type assessments show promise for differential predictive value. The present study included 70 individuals: 42 with idiopathic PD without dementia and 28 age- and education-matched healthy control adults (HC). Participants completed assessments of cognition with emphasis on tests that are sensitive to frontal and posterior deficits. PD patients were classified into cognitive subgroups and the subgroups were compared on demographic and disease variables. Individual performance across neuropsychological tests was evaluated for the PD group. Patients with PD performed more poorly than HC on several measures of cognition, and they were classified into frontal (12), posterior (3), both (10) and neither subgroups (17), the latter two in reference to frontal- and posterior-type deficits. The neither subgroup was distinguished by less motor impairment than the both subgroup, but the four subgroups did not otherwise differ on demographic or disease variables. Across patients, the tests most sensitive to cognitive impairment included measures of attention and executive functioning (frontal-type tests). Examination of individual test performance for PD revealed substantial heterogeneity across tests with respect to number and severity of deficits. The current study provides insight into which commonly used neuropsychological tests are most sensitive to cognitive deficits (strictly defined) in a nondemented, well characterized PD sample, and into the relation of cognitive subgroups to demographic and disease-specific variables.
2013-01-01T00:00:00ZEffects of Parkinson’s disease on optic flow perception for heading direction during navigation
https://hdl.handle.net/2144/34397
Effects of Parkinson’s disease on optic flow perception for heading direction during navigation
Lin, Cheng-Chieh; Wagenaar, Robert C.; Young, Daniel; Saltzman, Elliot L.; Ren, Xiaolin; Neargarder, Sandy; Cronin-Golomb, Alice
Visuoperceptual disorders have been identified in individuals with Parkinson’s disease (PD) and may affect the perception of optic flow for heading direction during navigation. Studies in healthy subjects have confirmed that heading direction can be determined by equalizing the optic flow speed (OS) between visual fields. The present study investigated the effects of PD on the use of optic flow for heading direction, walking parameters, and interlimb coordination during navigation, examining the contributions of OS and spatial frequency (dot density). Twelve individuals with PD without dementia, 18 age-matched normal control adults (NC), and 23 young control adults (YC) walked through a virtual hallway at about 0.8 m/s. The hallway was created by random dots on side walls. Three levels of OS (0.8, 1.2, and 1.8 m/s) and dot density (1, 2, and 3 dots/m2) were presented on one wall while on the other wall, OS and dot density were fixed at 0.8 m/s and 3 dots/m2, respectively. Three-dimensional kinematic data were collected, and lateral drift, walking speed, stride frequency and length, and frequency, and phase relations between arms and legs were calculated. A significant linear effect was observed on lateral drift to the wall with lower OS for YC and NC, but not for PD. Compared to YC and NC, PD veered more to the left under OS and dot density conditions. The results suggest that healthy adults perceive optic flow for heading direction. Heading direction in PD may be more affected by the asymmetry of dopamine levels between the hemispheres and by motor lateralization as indexed by handedness.
2014-01-01T00:00:00ZFunctional correlates of optic flow motion processing in Parkinson’s disease
https://hdl.handle.net/2144/34396
Functional correlates of optic flow motion processing in Parkinson’s disease
Putcha, Deepti; Ross, Robert S.; Rosen, Maya L.; Norton, Daniel J.; Cronin-Golomb, Alice; Somers, David C.; Stern, Chantal E.
The visual input created by the relative motion between an individual and the environment, also called optic flow, influences the sense of self-motion, postural orientation, veering of gait, and visuospatial cognition. An optic flow network comprising visual motion areas V6, V3A, and MT+, as well as visuo-vestibular areas including posterior insula vestibular cortex (PIVC) and cingulate sulcus visual area (CSv), has been described as uniquely selective for parsing egomotion depth cues in humans. Individuals with Parkinson’s disease (PD) have known behavioral deficits in optic flow perception and visuospatial cognition compared to age- and education-matched control adults (MC). The present study used functional magnetic resonance imaging (fMRI) to investigate neural correlates related to impaired optic flow perception in PD. We conducted fMRI on 40 non-demented participants (23 PD and 17 MC) during passive viewing of simulated optic flow motion and random motion. We hypothesized that compared to the MC group, PD participants would show abnormal neural activity in regions comprising this optic flow network. MC participants showed robust activation across all regions in the optic flow network, consistent with studies in young adults, suggesting intact optic flow perception at the neural level in healthy aging. PD participants showed diminished activity compared to MC particularly within visual motion area MT+ and the visuo-vestibular region CSv. Further, activation in visuo-vestibular region CSv was associated with disease severity. These findings suggest that behavioral reports of impaired optic flow perception and visuospatial performance may be a result of impaired neural processing within visual motion and visuo-vestibular regions in PD.
2014-01-01T00:00:00ZThe effect of Parkinson’s disease subgroups on verbal and nonverbal fluency
https://hdl.handle.net/2144/34395
The effect of Parkinson’s disease subgroups on verbal and nonverbal fluency
Jaywant, Abhishek; Musto, Giovanni; Neargarder, Sandy; Stavitsky Gilbert, Karina; Cronin-Golomb, Alice
BACKGROUND: Parkinson’s disease (PD) leads to deficits in executive function, including verbal and nonverbal fluency, as a result of compromised frontostriatal circuits. It is unknown whether deficits in verbal and nonverbal fluency in PD are driven by certain subgroups of patients, or how strategy use may facilitate performance. PARTICIPANTS: Sixty-five nondemented individuals with PD, including 36 with right-body onset (RPD; 20 with tremor as their initial symptom, 16 nontremor) and 29 with left-body onset (LPD; 14 with tremor as their initial symptom, 15 nontremor), and 52 normal control participants (NC) took part in the study. MEASUREMENTS: Verbal fluency was assessed using the FAS and Animals tests. Nonverbal fluency was assessed using the Ruff Figural Fluency Test. RESULTS: Both RPD and LPD were impaired in generating words and in using clustering and switching strategies on phonemic verbal fluency, whereas different patterns of impairment were found on nonverbal fluency depending on the interaction of side of onset and initial motor symptom (tremor vs. nontremor). Strategy use correlated with number of correct responses on verbal fluency in LPD, RPD, and NC. By contrast, on nonverbal fluency, strategy use correlated with correct responses for RPD and LPD, but not for NC. CONCLUSION: Our findings demonstrate the importance of considering subgroups in PD and analyzing subcomponents of verbal and nonverbal fluency (correct responses, errors, and strategies), which may depend differently on the integrity of dorsolateral prefrontal cortex, inferior frontal cortex, and anterior cingulate cortex.
2014-01-01T00:00:00ZAltered intrinsic functional coupling between core neurocognitive networks in Parkinson's disease
https://hdl.handle.net/2144/34394
Altered intrinsic functional coupling between core neurocognitive networks in Parkinson's disease
Putcha, Deepti; Ross, Robert S.; Cronin-Golomb, Alice; Janes, Amy C.; Stern, Chantal E.
Parkinson's disease (PD) is largely attributed to disruptions in the nigrostriatal dopamine system. These neurodegenerative changes may also have a more global effect on intrinsic brain organization at the cortical level. Functional brain connectivity between neurocognitive systems related to cognitive processing is critical for effective neural communication, and is disrupted across neurological disorders. Three core neurocognitive networks have been established as playing a critical role in the pathophysiology of many neurological disorders: the default-mode network (DMN), the salience network (SN), and the central executive network (CEN). In healthy adults, DMN-CEN interactions are anti-correlated while SN-CEN interactions are strongly positively correlated even at rest, when individuals are not engaging in any task. These intrinsic between-network interactions at rest are necessary for efficient suppression of the DMN and activation of the CEN during a range of cognitive tasks. To identify whether these network interactions are disrupted in individuals with PD, we used resting state functional magnetic resonance imaging (rsfMRI) to compare between-network connectivity between 24 PD participants and 20 age-matched controls (MC). In comparison to the MC, individuals with PD showed significantly less SN-CEN coupling and greater DMN-CEN coupling during rest. Disease severity, an index of striatal dysfunction, was related to reduced functional coupling between the striatum and SN. These results demonstrate that individuals with PD have a dysfunctional pattern of interaction between core neurocognitive networks compared to what is found in healthy individuals, and that interaction between the SN and the striatum is even more profoundly disrupted in those with greater disease severity.
2015-01-01T00:00:00ZEffect of visual cues on the resolution of perceptual ambiguity in Parkinson’s disease and normal aging
https://hdl.handle.net/2144/34393
Effect of visual cues on the resolution of perceptual ambiguity in Parkinson’s disease and normal aging
Díaz-Santos, Mirella; Cao, Bo; Mauro, Samantha A.; Yazdanbakhsh, Arash; Neargarder, Sandy; Cronin-Golomb, Alice
Parkinson's disease (PD) and normal aging have been associated with changes in visual perception, including reliance on external cues to guide behavior. This raises the question of the extent to which these groups use visual cues when disambiguating information. Twenty-seven individuals with PD, 23 normal control adults (NC), and 20 younger adults (YA) were presented a Necker cube in which one face was highlighted by thickening the lines defining the face. The hypothesis was that the visual cues would help PD and NC to exert better control over bistable perception. There were three conditions, including passive viewing and two volitional-control conditions (hold one percept in front; and switch: speed up the alternation between the two). In the Hold condition, the cue was either consistent or inconsistent with task instructions. Mean dominance durations (time spent on each percept) under passive viewing were comparable in PD and NC, and shorter in YA. PD and YA increased dominance durations in the Hold cue-consistent condition relative to NC, meaning that appropriate cues helped PD but not NC hold one perceptual interpretation. By contrast, in the Switch condition, NC and YA decreased dominance durations relative to PD, meaning that the use of cues helped NC but not PD in expediting the switch between percepts. Provision of low-level cues has effects on volitional control in PD that are different from in normal aging, and only under task-specific conditions does the use of such cues facilitate the resolution of perceptual ambiguity.
2015-02-01T00:00:00Z