Uniqueness theorems for a class of singular partial differential equations

Of fundamental importance in physics are problems whose mathematical formulation requires at least three dimensions. Since in many ways one and two dimensional problems are easier to handle, one of the major efforts of mathematicians has been to reduce three dimensional problems to those of lower dimensions. Fourier analysis, separation of variables, integral transforms, and the introduction of various kinds of axial symmetry are some of the more familiar methods that have been devised with this aim in mind. This thesis is concerned with the study of the two dimensional equations that result when Fourier analysis is applied to the three dimensional Helmholtz or reduced wave equation

What Cognitive Processes Drive Attentional Bias, and How Does Stress Affect Them?

Attentional biases toward or away from emotionally evocative stimuli have been well documented and related to clinical outcomes such as social anxiety. Some work has suggested that stress modulates attentional biases, but there are a number of inconsistencies in this literature regarding the direction of that modulation, highlighting a need to examine moderators of that effect. Sex differences in stress effects could potentially explain this inconsistency, as acute stress can affect males and females differently. It is also possible that stress differentially influences multiple component processes underpinning attentional bias, but these processes have not been well character, and to date no study has examined this possibility. We addressed these gaps by examining the effects of an acute stressor on attentional bias and its component processes, quantified by computational cognitive modeling, as well as potential sex differences in these effects. We found that overall participants were significantly biased towards threat, but biases did not differ by stress condition or sex. Additionally, we found evidence that attentional bias to threat is a function of both automatic and controlled attentional processes, but that stress did not influence these processes within the context of this task. These findings help to clarify the existing discrepancy in the literature, as differences in methods may differentially affect controlled and automatic attentional processes. Additionally, these findings provide a new avenue of researching attention to threat and the automatic processes that drive it

What Cognitive Processes Drive Attentional Bias, and How Does Stress Affect Them?

Attentional biases toward or away from emotionally evocative stimuli have been well documented and related to clinical outcomes such as social anxiety. Some work has suggested that stress modulates attentional biases, but there are a number of inconsistencies in this literature regarding the direction of that modulation, highlighting a need to examine moderators of that effect. Sex differences in stress effects could potentially explain this inconsistency, as acute stress can affect males and females differently. It is also possible that stress differentially influences multiple component processes underpinning attentional bias, but these processes have not been well character, and to date no study has examined this possibility. We addressed these gaps by examining the effects of an acute stressor on attentional bias and its component processes, quantified by computational cognitive modeling, as well as potential sex differences in these effects. We found that overall participants were significantly biased towards threat, but biases did not differ by stress condition or sex. Additionally, we found evidence that attentional bias to threat is a function of both automatic and controlled attentional processes, but that stress did not influence these processes within the context of this task. These findings help to clarify the existing discrepancy in the literature, as differences in methods may differentially affect controlled and automatic attentional processes. Additionally, these findings provide a new avenue of researching attention to threat and the automatic processes that drive it

Active Exterior Cloaking

A new method of cloaking is presented. For two-dimensional quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is approximately one within one disk and zero within a second disk, and such a polynomial is constructed. For the two-dimensional Helmholtz equation, it is numerically shown that three active exterior devices placed around the object suffice to produce very good cloaking.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Thermal Radiation From Carbon Nanotube in Terahertz Range

The thermal radiation from an isolated finite-length carbon nanotube (CNT) is theoretically investigated both in near- and far-field zones. The formation of the discrete spectrum in metallic CNTs in the terahertz range is demonstrated due to the reflection of strongly slowed-down surface-plasmon modes from CNT ends. The effect does not appear in semiconductor CNTs. The concept of CNT as a thermal nanoantenna is proposed.Comment: 5 pages, 3 figure

Inter-rater reliability for movement pattern analysis (MPA): measuring patterning of behaviors versus discrete behavior counts as indicators of decision-making style

The unique yield of collecting observational data on human movement has received increasing attention in a number of domains, including the study of decision-making style. As such, interest has grown in the nuances of core methodological issues, including the best ways of assessing inter-rater reliability. In this paper we focus on one key topic – the distinction between establishing reliability for the patterning of behaviors as opposed to the computation of raw counts – and suggest that reliability for each be compared empirically rather than determined a priori. We illustrate by assessing inter-rater reliability for key outcome measures derived from movement pattern analysis (MPA), an observational methodology that records body movements as indicators of decision-making style with demonstrated predictive validity. While reliability ranged from moderate to good for raw counts of behaviors reflecting each of two Overall Factors generated within MPA (Assertion and Perspective), inter-rater reliability for patterning (proportional indicators of each factor) was significantly higher and excellent (ICC = 0.89). Furthermore, patterning, as compared to raw counts, provided better prediction of observable decision-making process assessed in the laboratory. These analyses support the utility of using an empirical approach to inform the consideration of measuring patterning versus discrete behavioral counts of behaviors when determining inter-rater reliability of observable behavior. They also speak to the substantial reliability that may be achieved via application of theoretically grounded observational systems such as MPA that reveal thinking and action motivations via visible movement patterns

Predicting individual differences in decision-making process from signature movement styles: an illustrative study of leaders

There has been a surge of interest in examining the utility of methods for capturing individual differences in decision-making style. We illustrate the potential offered by Movement Pattern Analysis (MPA), an observational methodology that has been used in business and by the US Department of Defense to record body movements that provide predictive insight into individual differences in decision-making motivations and actions. Twelve military officers participated in an intensive 2-h interview that permitted detailed and fine-grained observation and coding of signature movements by trained practitioners using MPA. Three months later, these subjects completed four hypothetical decision-making tasks in which the amount of information sought out before coming to a decision, as well as the time spent on the tasks, were under the partial control of the subject. A composite MPA indicator of how a person allocates decision-making actions and motivations to balance both Assertion (exertion of tangible movement effort on the environment to make something occur) and Perspective (through movements that support shaping in the body to perceive and create a suitable viewpoint for action) was highly correlated with the total number of information draws and total response time—individuals high on Assertion reached for less information and had faster response times than those high on Perspective. Discussion focuses on the utility of using movement-based observational measures to capture individual differences in decision-making style and the implications for application in applied settings geared toward investigations of experienced leaders and world statesmen where individuality rules the day