Hecke algebras of finite type are cellular

Let \cH be the one-parameter Hecke algebra associated to a finite Weyl group $W$, defined over a ground ring in which ``bad'' primes for $W$ are invertible. Using deep properties of the Kazhdan--Lusztig basis of \cH and Lusztig's \ba-function, we show that \cH has a natural cellular structure in the sense of Graham and Lehrer. Thus, we obtain a general theory of ``Specht modules'' for Hecke algebras of finite type. Previously, a general cellular structure was only known to exist in types $A_n$ and $B_n$.Comment: 14 pages; added reference

On the idempotents of Hecke algebras

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion procedure for the Hecke algebras. We show that the normalization factors which occur in the procedure are related to the Ocneanu--Markov trace of the idempotents.Comment: 11 page

On the Representation Theory of an Algebra of Braids and Ties

We consider the algebra ${\cal E}_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for ${\cal E}_n(u)$ and show that this is faithful. We use it to give a basis for ${\cal E}_n(u)$ and to classify its irreducible representations.Comment: 24 pages. Final version. To appear in Journal of Algebraic Combinatorics

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki's categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial Z-grading on blocks of cyclotomic Hecke algebras, including symmetric groups in positive characteristic.Comment: 32 pages; minor changes to section

Deep Learning of Representations: Looking Forward

Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to impressive theoretical results, learning algorithms and breakthrough experiments, several challenges lie ahead. This paper proposes to examine some of these challenges, centering on the questions of scaling deep learning algorithms to much larger models and datasets, reducing optimization difficulties due to ill-conditioning or local minima, designing more efficient and powerful inference and sampling procedures, and learning to disentangle the factors of variation underlying the observed data. It also proposes a few forward-looking research directions aimed at overcoming these challenges

Carbon clusters near the crossover to fullerene stability

The thermodynamic stability of structural isomers of $\mathrm{C}_{24}$, $\mathrm{C}_{26}$, $\mathrm{C}_{28}$ and $\mathrm{C}_{32}$, including fullerenes, is studied using density functional and quantum Monte Carlo methods. The energetic ordering of the different isomers depends sensitively on the treatment of electron correlation. Fixed-node diffusion quantum Monte Carlo calculations predict that a $\mathrm{C}_{24}$ isomer is the smallest stable graphitic fragment and that the smallest stable fullerenes are the $\mathrm{C}_{26}$ and $\mathrm{C}_{28}$ clusters with $\mathrm{C}_{2v}$ and $\mathrm{T}_{d}$ symmetry, respectively. These results support proposals that a $\mathrm{C}_{28}$ solid could be synthesized by cluster deposition.Comment: 4 pages, includes 4 figures. For additional graphics, online paper and related information see http://www.tcm.phy.cam.ac.uk/~prck

Murchison Widefield Array rapid-response observations of the short GRB 180805A

Abstract Here we present stringent low-frequency (185 MHz) limits on coherent radio emission associated with a short-duration gamma-ray burst (SGRB). Our observations of the short gamma-ray burst (GRB) 180805A were taken with the upgraded Murchison Widefield Array (MWA) rapid-response system, which triggered within 20s of receiving the transient alert from the Swift Burst Alert Telescope, corresponding to 83.7 s post-burst. The SGRB was observed for a total of 30 min, resulting in a $3\sigma$ persistent flux density upper limit of 40.2 mJy beam–1. Transient searches were conducted at the Swift position of this GRB on 0.5 s, 5 s, 30 s and 2 min timescales, resulting in $3\sigma$ limits of 570–1 830, 270–630, 200–420, and 100–200 mJy beam–1, respectively. We also performed a dedispersion search for prompt signals at the position of the SGRB with a temporal and spectral resolution of 0.5 s and 1.28 MHz, respectively, resulting in a $6\sigma$ fluence upper-limit range from 570 Jy ms at DM $=3\,000$ pc cm–3 ( $z\sim 2.5$ ) to 1 750 Jy ms at DM $=200$ pc cm–3 ( $z\sim 0.1)$ , corresponding to the known redshift range of SGRBs. We compare the fluence prompt emission limit and the persistent upper limit to SGRB coherent emission models assuming the merger resulted in a stable magnetar remnant. Our observations were not sensitive enough to detect prompt emission associated with the alignment of magnetic fields of a binary neutron star just prior to the merger, from the interaction between the relativistic jet and the interstellar medium (ISM) or persistent pulsar-like emission from the spin-down of the magnetar. However, in the case of a more powerful SGRB (a gamma-ray fluence an order of magnitude higher than GRB 180805A and/or a brighter X-ray counterpart), our MWA observations may be sensitive enough to detect coherent radio emission from the jet-ISM interaction and/or the magnetar remnant. Finally, we demonstrate that of all current low- frequency radio telescopes, only the MWA has the sensitivity and response times capable of probing prompt emission models associated with the initial SGRB merger event.</jats:p

EFFECT OF CORTISOL TREATMENT ON HORMONAL RELATIONSHIPS IN CONGENITAL ADRENAL HYPERPLASIA

The temporal relationship between administration of cortisol and serum 17Α-hydroxyprogesterone was investigated in five patients aged 9-19 years with congenital adrenal hyperplasia due to 21-hydroxylase deficiency. There was marked variability in the 17Α-hydroxyprogesterone response (determined hourly for 24 h) of individual patients to administration of cortisol. Mean concentration was less than 0.030 Μmol/l in one patient but 0.519Μ mol/l in another. Levels were higher in all patients while off treatment, and were greatest in those with salt-losing adrenal hyperplasia. Growth hormone secretion was not suppressed by treatment with cortisol. Withdrawal of cortisol for 3 days resulted in a significant decrease in the mean serum FSH/LH ratio and a rise in serum testosterone in all subjects. Episodic release of gonadotrophins persisted in the adolescent patients.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75713/1/j.1365-2265.1977.tb02002.x.pd