Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations

Character expansion expresses extended HOMFLY polynomials through traces of products of finite dimensional R- and Racah mixing matrices. We conjecture that the mixing matrices are expressed entirely in terms of the eigenvalues of the corresponding R-matrices. Even a weaker (and, perhaps, more reliable) version of this conjecture is sufficient to explicitly calculate HOMFLY polynomials for all the 3-strand braids in arbitrary (anti)symmetric representations. We list the examples of so obtained polynomials for V=[3] and V=[4], and they are in accordance with the known answers for torus and figure-eight knots, as well as for the colored special and Jones polynomials. This provides an indirect evidence in support of our conjecture.Comment: 20 pages + 21 pages of knot table

Mystics Duo for two pianos

To celebrate Alexander Scriabin’s (1872-1915) anniversary year, his Mystic Chord: C, D, E, F#, A, Bb was used as the primary pitch material within this work. A Mystic Complement: Db, Eb, F, G, Ab, B completed the total chromatic and provided secondary pitch material used for contrast and balance. A pair of pitch matrices was generated from the Chord and Complement and the resulting materials were subdivided across the movements. This piano duo carries the listener through three movements of succinct and well-focused musical form

Recoil

Recoil examines my personal experiences in recovering from a car accident. The word ‘recoil’ is used in two senses: to change speed and direction as a result of a collision; to shrink in fear. The work represents a labyrinth of memory, where the fragmented self confronts distorted realities and fearful illusions. Recoil builds upon the harmonic explorations of my string quartet Impacts and Fractures (1999): a ‘dominant seventh’ chord, partials 4-7 of the harmonic series, is tempered to the quarter-tone scale and elaborated to create a series of complex modes. These modes regulate all the melodic and harmonic material for both the soloist and the tape part. The tape part is derived entirely from the processed recording of an acoustic piano, and takes the role of a superinstrument that confronts, encompasses and absorbs the soloist. The work is a result of the extensive analysis and processing of melodic fragments, performed on the piano by myself, employing the recent IRCAM program ‘Audiosculpt’. These fragments are: transposed by microintervals to produce a harmonically rich chorus of arabesques; independently modified in pitch and tempo to realise rhythmically complex dialogues with the soloist; filtered and transposed to create a continuum of sounds ranging from a recognisable piano towards noise; greatly expanded in length to reveal a gradually unfolding, haunting soundworld. Spatialisation is central to the concept of the work: sounds are carefully positioned and moved in space to produce an unreal acoustic labyrinth surrounding the soloist

Adult mortality and investment: a new explanation of the English agricultural productivity in the 18th century

We claim that the exogenous decline of adult mortality at the end of the seventeenth century can be one of the causes driving both the decline of interest rate and the increase in agricultural production per acre in preindustrial England. Following the intuition of the life-cycle hypothesis, we show that the increase in adult life expectancy must have implied less farmer impatience and it could have caused more investment in nitrogen stock and land fertility, and higher production per acre. We analyse this dynamic interaction using an overlapping generation model and show that the evolution of agricultural production and capital rates of return predicted by the model coincide fairly well with their empirical pattern

Resonance assignments for latherin, a natural surfactant protein from horse sweat

Latherin is an intrinsically surfactant protein of ~23 kDa found in the sweat and saliva of horses. Its function is probably to enhance the translocation of sweat water from the skin to the surface of the pelt for evaporative cooling. Its role in saliva may be to enhance the wetting, softening and maceration of the dry, fibrous food for which equines are adapted. Latherin is unusual in its relatively high content of aliphatic amino acids (~25 % leucines) that might contribute to its surfactant properties. Latherin is related to the palate, lung, and nasal epithelium carcinoma-associated proteins (PLUNCs) of mammals, at least one of which is now known to exhibit similar surfactant activity to latherin. No structures of any PLUNC protein are currently available. 15N,13C-labelled recombinant latherin was produced in Escherichia coli, and essentially all of the resonances were assigned despite the signal overlap due to the preponderance of leucines. The most notable exceptions include a number of residues located in an apparently dynamic loop region between residues 145 and 154. The assignments have been deposited with BMRB accession number 19067

Minimal symmetric differences of lines in projective planes

Let q be an odd prime power and let f(r) be the minimum size of the symmetric difference of r lines in the Desarguesian projective plane PG(2,q). We prove some results about the function f(r), in particular showing that there exists a constant C>0 such that f(r)=O(q) for Cq^{3/2}<r<q^2 - Cq^{3/2}.Comment: 16 pages + 2 pages of tables. This is a slightly revised version of the previous one (Thm 6 has been improved, and a few points explained

Huntington’s Disease iPSC-Derived Brain Microvascular Endothelial Cells Reveal WNT-Mediated Angiogenic and Blood-Brain Barrier Deficits

Brain microvascular endothelial cells (BMECs) are an essential component of the blood-brain barrier (BBB) that shields the brain against toxins and immune cells. While BBB dysfunction exists in neurological disorders, including Huntington's disease (HD), it is not known if BMECs themselves are functionally compromised to promote BBB dysfunction. Further, the underlying mechanisms of BBB dysfunction remain elusive given limitations with mouse models and post-mortem tissue to identify primary deficits. We undertook a transcriptome and functional analysis of human induced pluripotent stem cell (iPSC)-derived BMECs (iBMEC) from HD patients or unaffected controls. We demonstrate that HD iBMECs have intrinsic abnormalities in angiogenesis and barrier properties, as well as in signaling pathways governing these processes. Thus, our findings provide an iPSC-derived BBB model for a neurodegenerative disease and demonstrate autonomous neurovascular deficits that may underlie HD pathology with implications for therapeutics and drug delivery.American Heart Association (12PRE10410000)American Heart Association (CIRMTG2-01152)National Institutes of Health (U.S.) (NIHNS089076