The Squares: US Physical and Engineering Scientists in the Long 1970s, Cyrus C. M. Mody, MIT Press, 2022. Open access ($65.00 paper)

Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filter-based solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement matrix into square root form. Such techniques ...

The online square detection problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. Recall that a square is a string that is a concatenation of two identical strings. In this paper we present an algorithm solving this problem in O(n log σ) time and linear space on ordered alphabet, where σ is the number of different letters in the ...

Quantitative eye movement recordings in a patient with multiple sclerosis who had both macro square wave jerks and an internuclear ophthalmoparesis supported the concept of an internal brain-stem monitor that mediates corrective eye movements. A brain-stem model of this monitor illustrates the patient's motility disorder and the normal function of providing synergistic version and vergence corr...

A word w is rich if it has |w| + 1 many distinct palindromic factors, including the empty word. A word is square-free if it does not have a factor uu, where u is a non-empty word. Pelantová and Starosta (Discrete Math. 313 (2013)) proved that every infinite rich word contains a square. We will give another proof for that result. Pelantová and Starosta denoted by r(n) the length of a longest ric...

Square Root Palindromes ................................... 1 Sigma Quest .......................................................... 6 Decimal Fractions ................................................ 9 Designing Weavable Color Patterns ............... 12 Polygraphic Substitution .................................. 17 Programming Tips ............................................. 20 What’s Comi...

The almost square rectangle packing problem involves packing all rectangles with sizes 1 × 2 to n × (n + 1) (almost squares) into an enclosing rectangle with minimal area. This extends the previously studied square packing problem by adding an additional degree of freedom for each rectangle, deciding in which orientation the item should be packed. We show how to extend the model and search stra...

Below a (comparatively large) measure of non-Hermiticity Z = Z (crit) 0 > 0 of a PT symmetrically complexified square well, bound states are constructed non-numerically. All their energies prove real and continuous in the (Hermitian) limit Z → 0. Beyond the threshold Z (crit) 0 (and, in general, beyond Z (crit) m at m = 0, 1, . . .) the lowest two real energies (i.e., E2m and E2m+1) are shown t...

A A-linked design is an abstract system of v 'points' and b lines' such that every two points are joined by exactly A lines. A partial classification is given of those extremal examples with b = v, and necessary and sufficient conditions are proved for them to be of each of the only two non-trivial types known, namely square BIBDs and point-complemented square BIBDs. For each A > 1 the number o...