Design and Implementation of Digital Beam Former Architecture for Phased Array Radar

This paper deals with the design and implementation of a digital beam former architecture which is developed for 4/8/12/16 element phased array radar. This technique employs a very high performance FPGA to handle large no of parallel complex arithmetic operations including digital down conversion and filtering. A 3MHz echo signal riding on an IF carrier of 60 MHz is under sampled at 50 MHz and down converted digitally to bring the spectrum to echo signal baseband. After suitable decimation filtering, the I and Q channels are multiplied with Recursive Least Squares based optimized complex weights to form partial beams. The prototype architecture employs techniques of pipelining and parallelism to generate multiple beams simultaneously from a 16 element array within 1 μsec. This can be extended to several number of arrays. The critical components employed in this design are eight 16 bit 125 MS/s ADCs and a very high performance state of the art Xilinx FPGA device Virtex-5 FX 130T having several on-chip resources and 150 MHz clock generators.

Anxiety-Related Difficulties With Complex Arithmetic

Human behavior depends on the interplay between cognition and emotion. Negative emotions like anxiety affect performance, particularly in complex tasks, by limiting cognitive resources – known as the anxiety–complexity effect. This study set out to replicate the anxiety–complexity effect in a web-based experiment. We investigated individual differences in math anxiety – a negative emotional response specific to math – and arithmetic performance ( N = 382). The mental arithmetic task consisted of a two-digit addition and subtraction, with/without carrying or borrowing, respectively. As expected and preregistered, higher math anxiety was related to poorer arithmetic performance, especially in complex tasks – indicating the anxiety–complexity effect. Consequently, the negative math anxiety-performance link is especially pronounced for complex arithmetic, which requires calculations across place-values and thus working memory resources. This successful replication of the anxiety–complexity effect suggests that math-anxious individuals have particular difficulties in complex arithmetic.

Ancient visual channels have a causal role in arithmetic calculations

Humans exhibit complex arithmetic skills, often attributed to our exceptionally large neocortex. However, the past decade has provided ample evidence that the functional domain of the subcortex extends well beyond basic functions. Using a sensitive behavioral method, for the first time, we explored the contributions of lower-order visual monocular channels to symbolic arithmetic operations, addition and subtraction. The pattern of results from 4 different experiments provides converging evidence for a causal relation between mental arithmetic and primitive subcortical regions. The results have major implications for our understanding of the neuroevolutionary development of general numerical abilities–subcortical regions, which are shared across different species, are essential to complex numerical operations. In a bigger conceptual framework, these findings and others call for a shift from the modal view of the exclusive role of the neocortex in high-level cognition to a view that emphasizes the interplay between subcortical and cortical brain networks.

Fuzzy logical conclusions and conclusions in expert systems of medical diagnostics

The main problems in making a correct diagnosis are: subjectivity and insufficient qualifications of the doctor, difficulties in correctly assessing the patient’s complaints, signs and symptoms of the disease observed in the patient, as well as individual manifestations of the symptoms of the disease. In publications on the use of expert systems for medical diagnostics using fuzzy logic, the main attention was paid to the medical features of the problem. In this work, for the first time, general methodological aspects of building such systems, creating databases, representing by fuzzy sets of real numbers, digital scales, linguistic and Boolean data of symptom values are formulated. The types of membership functions that are advisable to use to represent the symptoms of diseases are proposed. In fuzzy-logical conclusions, not only the values of the characteristic functions of the logical terms of individual symptoms, but also complex arithmetic functions of their values are used.

The Demands of Simple and Complex Arithmetic Word Problems on Language and Cognitive Resources

Solving arithmetic word problems requires constructing a situation model based on the problem text and translating that into a mathematical model. As such, word problem solving makes demands on students’ language comprehension and their domain-general cognitive resources. These demands may decrease when students get more experienced and use strategies that do not require fully understanding the situation presented in the problem. The current study aims to address this hypothesis. Students (N=444) from third to sixth grade solved a paper-and-pencil task with 48 mathematics problems, comprising symbolic arithmetic problems and standard word problems, as well as more complex word problems that involve two arithmetic steps or include irrelevant numerical information. Their performance was analyzed with multilevel logistic regression analyses. Results showed that within each grade, performance on the different problem types did not differ, suggesting that already in third-grade students seem helped nor hindered by presenting arithmetic problems in a story, even if that story contains irrelevant numerical information. Non-verbal reasoning was more important in standard word problems than in arithmetic problems in symbolic format in one-step arithmetic, and reading comprehension was more important in solving two-step arithmetic word problems than in one-step arithmetic word problems.

The Origins of Human Complex Arithmetic Abilities: Involvement of Evolutionarily Ancient Brain Circuits

Humans exhibit complex arithmetic skills, often attributed to the exceptional enlargement of neocortical regions during evolution. However, the past decade has provided ample evidence that the functional domain of the subcortex extend well beyond basic functions. Using a sensitive behavioral method, for the first time, we explored the contributions of lower-order visual monocular channels to symbolic arithmetic operations, addition and subtraction. The pattern of results from 4 different experiments provides converging evidence for a causal relation between mental arithmetic and primitive subcortical regions. The results have major implications for our understanding of the neuroevolutionary development of general numerical abilities–subcortical regions, which are shared across different species, are essential to complex numerical operations. In a bigger conceptual framework, these findings and others call for a shift from the modal view of the exclusive role of the neocortex in high-level cognition to a view that emphasizes the interplay between subcortical and cortical brain networks.

Primitive visual channels have a causal role in cognitive transfer

Scientific investigations have long emphasized the cortex’s role in cognitive transfer and arithmetic abilities. To date, however, this assumption has not been thoroughly empirically investigated. Here we demonstrated that primitive mechanisms—lower visual channels—have a causal role in cognitive transfer of complex skills such as symbolic arithmetic. We found that exposing only one monocular channel to a visuospatial training resulted in a larger transfer effect in the trained monocular channel compared to the untrained monocular channel. Such cognitive transfer was found for both novel figural-spatial problems (near transfer) and novel subtraction problems (far transfer). Importantly, the benefits of the trained eye were not observed in old problems and in other tasks that did not involve visuospatial abilities (the Stroop task, a multiplication task). These results challenge the exclusive role of the cortex in cognitive transfer and complex arithmetic. In addition, the results suggest a new mechanism for the emergence of cognitive skills, that could be shared across different species.

Three addend addition: Who goes out of order and why?

Single-digit, three addend sums of the type a + b + c offer a rich opportunity to directly observe the range of strategies that different participants may use because they afford the possibility of measuring a partial sum (i.e., a + b or a + c or b + c). For example, while computing the sum 9 + 7 + 1, do participants go in order by first adding 9 + 7 and then adding 1, or do they incur the cost of going out of order by adding 9 + 1 in order to obtain the partial sum of 10, which makes the subsequent addition of 7 less effortful? Informed by findings in simple and complex arithmetic, we investigated the problem types and participant characteristics that can predict out of order switching behavior in such three-addend sums. To test our hypotheses, we tasked participants, first in an online study, and then in an in-person study to complete 120 single-digit, three addend problems. We found that participants switched the order of addition to prioritize efficiency gains in contexts in which the partial sum addends were small or equal to each other, or when doing so led to a partial sum of 10, or led to a partial sum that is equal to the third remaining integer. Response latency data confirmed that participants were deriving efficiencies in the manner we expected. Related to individual differences, our findings showed that participants with higher levels of math education were most likely to seek efficiency benefits whenever they were on offer.

What Deters Online Grocery Shopping? Investigating the Effect of Arithmetic Complexity and Product Type on User Satisfaction

This paper explores the influence of product type and arithmetic task complexity on users’ perceived mental effort and satisfaction in the context of online grocery shopping. A two-factor within-subject experiment was conducted with 32 participants. Results show that experience products and complex arithmetic tasks are associated with higher perceived mental effort compared to search products and simple arithmetic tasks. Perceived mental effort and satisfaction are negatively related. The more cognitive effort users need to invest in their online shopping tasks, the less satisfied they are likely to be with their online experience. Our results suggest that cognitive absorption mediates the relationship between cognitive effort and satisfaction. The study contributes to our understanding of online grocery shopping by explaining the effect of arithmetic complexity and product type on user satisfaction. It also offers shopping website designers a way to improve consumers’ online grocery shopping experience by implementing simple technology features in their websites to help users reduce their mental effort.

An optical neural chip for implementing complex-valued neural network

Complex-valued neural networks have many advantages over their real-valued counterparts. Conventional digital electronic computing platforms are incapable of executing truly complex-valued representations and operations. In contrast, optical computing platforms that encode information in both phase and magnitude can execute complex arithmetic by optical interference, offering significantly enhanced computational speed and energy efficiency. However, to date, most demonstrations of optical neural networks still only utilize conventional real-valued frameworks that are designed for digital computers, forfeiting many of the advantages of optical computing such as efficient complex-valued operations. In this article, we highlight an optical neural chip (ONC) that implements truly complex-valued neural networks. We benchmark the performance of our complex-valued ONC in four settings: simple Boolean tasks, species classification of an Iris dataset, classifying nonlinear datasets (Circle and Spiral), and handwriting recognition. Strong learning capabilities (i.e., high accuracy, fast convergence and the capability to construct nonlinear decision boundaries) are achieved by our complex-valued ONC compared to its real-valued counterpart.