Avoiding Rotated Bitboards with Direct Lookup

This paper describes an approach for obtaining direct access to the attacked squares of sliding pieces without resorting to rotated bitboards. The technique involves creating four hash tables using the built in hash arrays from an interpreted, high level language. The rank, file, and diagonal occupancy are first isolated by masking the desired portion of the board. The attacked squares are then directly retrieved from the hash tables. Maintaining incrementally updated rotated bitboards becomes unnecessary as does all the updating, mapping and shifting required to access the attacked squares. Finally, rotated bitboard move generation speed is compared with that of the direct hash table lookup method.Comment: 7 pages, 1 figure, 4 listings; replaced test positions, fixed typo

Variability in Exposure to Subspecialty Rotations During Orthopaedic Residency: A Website-based Review of Orthopaedic Residency Programs.

IntroductionThe variability in exposure to various subspecialty rotations during orthopaedic residency across the United States has not been well studied.MethodsData regarding program size, resident's sex, department leadership, university-based status of the program, outsourcing of subspecialty rotation, and geographic location were collected from websites of 151 US allopathic orthopaedic residency programs. The relationship of these factors with the time allotted for various clinical rotations was analyzed.ResultsThe number of residents in a program correlated positively with time allocated for elective rotations (r = 0.57, P = 0.0003). Residents in programs where the program director was a general orthopaedic surgeon spent more time on general orthopaedic rotations (22 versus 9.9 months, P = 0.001). Programs where the program director or chairman was an orthopaedic oncologist spent more time on oncology rotations ([3.8 versus 3 months, P = 0.01] and [3.5 versus 2.7 months, P = 0.01], respectively). Residents in community programs spent more time on adult reconstruction than university-based programs (6.6 versus 5.5 months, P = 0.014). Based on multiple linear regression analysis, time allotted for adult reconstruction (t = 2.29, P = 0.02) and elective rotations (t = 2.43, P = 0.017) was positively associated with the number of residents in the program.ConclusionsSubstantial variability exists in the time allocated to various clinical rotations during orthopaedic residency. The effect of this variability on clinical competence, trainees' career choices, and quality of patient care needs further study

New Symmetries in Crystals and Handed Structures

For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and counterclockwise directions as a distinct symmetry operation, here we show that there are many more structural symmetries than are currently recognized in right- or left-handed handed helices, spirals, and in antidistorted structures composed equally of rotations of both handedness. For example, though a helix or spiral cannot possess conventional mirror or inversion symmetries, they can possess them in combination with the rotation reversal symmetry. Similarly, we show that many antidistorted perovskites possess twice the number of symmetry elements as conventionally identified. These new symmetries predict new forms for "roto" properties that relate to static rotations, such as rotoelectricity, piezorotation, and rotomagnetism. They also enable symmetry-based search for new phenomena, such as multiferroicity involving a coupling of spins, electric polarization and static rotations. This work is relevant to structure-property relationships in all material structures with static rotations such as minerals, polymers, proteins, and engineered structures.Comment: 15 Pages, 4 figures, 3 Tables; Fig. 2b has error

Elko under spatial rotations

Under a rotation by an angle $\vartheta$, both the right- and left- handed Weyl spinors pick up a phase factor ${\exp(\pm\, i \vartheta/2)}$. The upper sign holds for the positive helicity spinors, while the lower sign for the negative helicity spinors. For $\vartheta = 2\pi$ radians this produces the famous minus sign. However, the four-component spinors are built from a direct sum of the indicated two-component spinors. The effect of the rotation by $2\pi$ radians on the eigenspinors of the parity - that is, the Dirac spinors -- is the same as on Weyl spinors. It is because for these spinors the right- and left- transforming components have the same helicity. And the rotation induced phases, being same, factor out. But for the eigenspinors of the charge conjugation operator, i.e. Elko, the left- and right- transforming components have opposite helicities, and therefore they pick up opposite phases. As a consequence the behaviour of the eigenspinors of the charge conjugation operator (Elko) is more subtle: for $0<\vartheta<2\pi$ a self conjugate spinor becomes a linear combination of the self and antiself conjugate spinors with $\vartheta$ dependent superposition coefficients - and yet the rotation preserves the self/antiself conjugacy of these spinors! This apparently paradoxical situation is fully resolved. This new effect, to the best of our knowledge, has never been reported before. The purpose of this communication is to present this result and to correct an interpretational error of a previous version.Comment: 7 pages, Two new sections, and significantly new material. An error in v1 and v2 correcte

RoboPol: Connection between optical polarization plane rotations and gamma-ray flares in blazars

We use results of our 3 year polarimetric monitoring program to investigate the previously suggested connection between rotations of the polarization plane in the optical emission of blazars and their gamma-ray flares in the GeV band. The homogeneous set of 40 rotation events in 24 sources detected by {\em RoboPol} is analysed together with the gamma-ray data provided by {\em Fermi}-LAT. We confirm that polarization plane rotations are indeed related to the closest gamma-ray flares in blazars and the time lags between these events are consistent with zero. Amplitudes of the rotations are anticorrelated with amplitudes of the gamma-ray flares. This is presumably caused by higher relativistic boosting (higher Doppler factors) in blazars that exhibit smaller amplitude polarization plane rotations. Moreover, the time scales of rotations and flares are marginally correlated.Comment: 12 pages, 16 figures, accepted to MNRA

Hamiltonian Pseudo-rotations of Projective Spaces

The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of ${\mathbb C}{\mathbb P}^n$ with the minimal possible number of periodic points (equal to $n+1$ by Arnold's conjecture), called here Hamiltonian pseudo-rotations. We prove several results on the dynamics of pseudo-rotations going beyond periodic orbits, using Floer theoretical methods. One of these results is the existence of invariant sets in arbitrarily small punctured neighborhoods of the fixed points, partially extending a theorem of Le Calvez and Yoccoz and Franks to higher dimensions. The other is a strong variant of the Lagrangian Poincar\'e recurrence conjecture for pseudo-rotations. We also prove the $C^0$-rigidity of pseudo-rotations with exponentially Liouville mean index vector. This is a higher-dimensional counterpart of a theorem of Bramham establishing such rigidity for pseudo-rotations of the disk.Comment: 38 pages; final version (with minor revisions and updated references); published Online First in Inventiones mathematica

Designing Optimal Perovskite Structure for High Ionic Conduction.

Solid-oxide fuel/electrolyzer cells are limited by a dearth of electrolyte materials with low ohmic loss and an incomplete understanding of the structure-property relationships that would enable the rational design of better materials. Here, using epitaxial thin-film growth, synchrotron radiation, impedance spectroscopy, and density-functional theory, the impact of structural parameters (i.e., unit-cell volume and octahedral rotations) on ionic conductivity is delineated in La0.9 Sr0.1 Ga0.95 Mg0.05 O3- δ . As compared to the zero-strain state, compressive strain reduces the unit-cell volume while maintaining large octahedral rotations, resulting in a strong reduction of ionic conductivity, while tensile strain increases the unit-cell volume while quenching octahedral rotations, resulting in a negligible effect on the ionic conductivity. Calculations reveal that larger unit-cell volumes and octahedral rotations decrease migration barriers and create low-energy migration pathways, respectively. The desired combination of large unit-cell volume and octahedral rotations is normally contraindicated, but through the creation of superlattice structures both expanded unit-cell volume and large octahedral rotations are experimentally realized, which result in an enhancement of the ionic conductivity. All told, the potential to tune ionic conductivity with structure alone by a factor of ≈2.5 at around 600 °C is observed, which sheds new light on the rational design of ion-conducting perovskite electrolytes