Quantitative Comparative Statics by Relative Derivatives on IS-LM with Five Production Factors Containing Multiple Energy Sources

Abstract This paper applies our established analytic technique of the relative derivative, (dy/dx)(a/b), to a quantitative comparative static analysis of a macroeconomy as based on the IS-LM framework coupled with a production function of five factors, capital, labor, oil, coal, and solar energy, resulting in twelve linear equations containing the general equilibrium growth rates of twelve endogenous variables, which are the six pairs of the (price, quantity) for the above output and five inputs. We conduct several simulations by substituting economically sensible values into all the parameters with some alterations for mathematical comparison, and finally we conclude with a summary remark. Mathematics Subject Classification: 91B02, 26B10, 91B62, 91B64, 91B7

Regression, Model Misspecification and Causation, with Pedagogical Demonstration

Abstract This paper shows, by a proposition and a numerical example, how a classic simple or multiple normal regression can achieve with 0.99 probability a near perfect fit to a random sample of any size but due to the omission of an independent variable the signs of the estimated coefficients are all wrong, thus distinguishing prediction from causation

Characterization of neurophysiologic and neurocognitive biomarkers for use in genomic and clinical outcome studies of schizophrenia.

BackgroundEndophenotypes are quantitative, laboratory-based measures representing intermediate links in the pathways between genetic variation and the clinical expression of a disorder. Ideal endophenotypes exhibit deficits in patients, are stable over time and across shifts in psychopathology, and are suitable for repeat testing. Unfortunately, many leading candidate endophenotypes in schizophrenia have not been fully characterized simultaneously in large cohorts of patients and controls across these properties. The objectives of this study were to characterize the extent to which widely-used neurophysiological and neurocognitive endophenotypes are: 1) associated with schizophrenia, 2) stable over time, independent of state-related changes, and 3) free of potential practice/maturation or differential attrition effects in schizophrenia patients (SZ) and nonpsychiatric comparison subjects (NCS). Stability of clinical and functional measures was also assessed.MethodsParticipants (SZ n = 341; NCS n = 205) completed a battery of neurophysiological (MMN, P3a, P50 and N100 indices, PPI, startle habituation, antisaccade), neurocognitive (WRAT-3 Reading, LNS-forward, LNS-reorder, WCST-64, CVLT-II). In addition, patients were rated on clinical symptom severity as well as functional capacity and status measures (GAF, UPSA, SOF). 223 subjects (SZ n = 163; NCS n = 58) returned for retesting after 1 year.ResultsMost neurophysiological and neurocognitive measures exhibited medium-to-large deficits in schizophrenia, moderate-to-substantial stability across the retest interval, and were independent of fluctuations in clinical status. Clinical symptoms and functional measures also exhibited substantial stability. A Longitudinal Endophenotype Ranking System (LERS) was created to rank neurophysiological and neurocognitive biomarkers according to their effect sizes across endophenotype criteria.ConclusionsThe majority of neurophysiological and neurocognitive measures exhibited deficits in patients, stability over a 1-year interval and did not demonstrate practice or time effects supporting their use as endophenotypes in neural substrate and genomic studies. These measures hold promise for informing the "gene-to-phene gap" in schizophrenia research

Teaching for learning with technology: a faculty development initiative at a research university

This paper reviews recent literature addressing the state of technology in higher education as a backdrop for a faculty development program offered annually at Northwestern. First, we will present the state of technology related to teaching in three areas: (1) the varied institutional interest in technology, (2) the variance in faculty engagement with technology, and (3) factors that influence faculty acceptance of technology. Next, we will introduce Northwestern’s response to the need for faculty development related to technology, the 5-day Teaching and Learning with Technology workshop. Finally, we will present data gathered over two years that demonstrates how pedagogically-driven technology training can enhance teaching and encourage faculty to embrace technology in teaching to accomplish pedagogically-based learning objectives

Relationships between changes in sustained fronto-striatal connectivity and positive affect with antidepressant treatment in major depression

Objective: Deficits in positive affect and their neural bases have been associated with major depression. However, whether reductions in positive affect result solely from an overall reduction in nucleus accumbens activity and fronto-striatal connectivity or the additional inability to sustain engagement of this network over time is unknown. The authors sought to determine whether treatment-induced changes in the ability to sustain nucleus accumbens activity and fronto-striatal connectivity during the regulation of positive affect are associated with gains in positive affect. Method: Using fMRI, the authors assessed the ability to sustain activity in reward-related networks when attempting to increase positive emotion during per- formance of an emotion regulation para- digm in 21 depressed patients before and after 2 months of antidepressant treat- ment. Over the same interval, 14 healthy comparison subjects underwent scanning as well. Results: After 2 months of treatment, self-reported positive affect increased. The patients who demonstrated the largest increases in sustained nucleus accumbens activity over the 2 months were those who demonstrated the largest increases in positive affect. In addition, the patients who demonstrated the largest increases in sustained fronto-striatal connectivity were also those who demonstrated the largest increases in positive affect when control- ling for negative affect. None of these associations were observed in healthy comparison subjects. Conclusions: Treatment-induced change in the sustained engagement of fronto- striatal circuitry tracks the experience of positive emotion in daily life. Studies examining reduced positive affect in a va- riety of psychiatric disorders might benefit from examining the temporal dynamics of brain activity when attempting to under- stand changes in daily positive affect

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}