We generalize the classical Cayley-Dickson doubling process starting with a quaternion algebra over a field F by allowing the scalar in the doubling to be an invertible element in the algebra. We investigate the resulting eight-dimensional algebras over F and show that they are division algebras for all scalars chosen in D outside of the base field F , if D is a division algebra.

The hypothesis that episodic memory retrieval can occur in parallel with other cognitive processes was tested in 2 experiments. Participants memorized words and then performed speeded cued recall (Experiment 1) or speeded yes-no recognition (Experiment 2) in a dual-task situation. The psychological refractory period design was used: The participant was presented with a single test item at vario...

The internal state of RC4 stream cipher is a permutation over ZN and its state transition is effectively a transposition or swapping of two elements. How the randomness of RC4 state evolves due to its state transitions has been studied for many years. As the number of swaps increases, the state comes closer to a uniform random permutation. We call the burn-in period of RC4 state transition as t...

Adequate circulating calcium (Ca) concentrations throughout the transition period are necessary for a productive lactation, but large quantities of Ca are lost from maternal Ca pools into milk and colostrum. A rapid, substantial drop in maternal blood Ca causes 5-10% of cows to be afflicted with clinical hypocalcemia (CH) and an additional 50% to suffer from subclinical hypocalcemia (SCH). Subc...

The Dimension Action (DA) model asserts that the visual system is modular, and that each task involves multiple-response mechanisms rather than a unitary-response selection mechanism. The model has been supported by evidence from single-task interference paradigms. We use the psychological refractory period paradigm and show that dual-task performance can also be explained by the DA model. In 6...

In a seminal STOC’95 paper, Arya et al. conjectured that spanners for low-dimensional Euclidean spaces with constant maximum degree, hop-diameter O(logn) and lightness O(logn) (i.e., weight O(logn)· w(MST)) can be constructed in O(n logn) time. This conjecture, which became a central open question in this area, was resolved in the affirmative by Elkin and Solomon in STOC’13 (even for doubling m...

It has recently been demonstrated that a lateralized distractor that matches the individual's top-down control settings elicits an N2pc wave, an electrophysiological index of the focus of visual-spatial attention, indicating that contingent capture has a visual-spatial locus. Here, we investigated whether contingent capture required capacity-limited central resources by incorporating a continge...

It is widely acknowledged that visual input is processed along two anatomically and functionally distinct pathways--a ventral pathway for conscious perception and a dorsal pathway for action control. The present study investigated whether the apparent direct and unmediated processing in the dorsal stream is subject to capacity limitations. Specifically, we tested whether a simple dorsal task of...