Zobrazeno 1 - 10
of 157
pro vyhledávání: '"Braden, P. W."'
Autor:
Braden, H. W., Disney-Hogg, Linden
We show that any $SU(2)$ BPS monopole of charge $k$ with rotational spatial dihedral symmetry is gauge equivalent to the Nahm data obtained from affine Toda equations of $C_l^{(1)}$ type when $k=2l$ or $A_{2(l-1)}^{(2)}$ type when $k=2l-1$.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/2407.20747
Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant bombardment
Externí odkaz:
http://arxiv.org/abs/2406.07445
Autor:
Braden, H. W., Disney-Hogg, Linden
The theta characteristics on a Riemann surface are permuted by the induced action of the automorphism group, with the orbit structure being important for the geometry of the curve and associated manifolds. We describe two new methods for advancing th
Externí odkaz:
http://arxiv.org/abs/2404.09890
The space of possible behaviors complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is a prominen
Externí odkaz:
http://arxiv.org/abs/2305.07482
Autor:
Braden, H. W., Disney-Hogg, Linden
Publikováno v:
Lett Math Phys 113, 87 (2023)
We classify all possible charge-3 monopole spectral curves with non-trivial automorphism group and within these identify those with elliptic quotients. By focussing on elliptic quotients the transcendental constraints for a monopole spectral curve be
Externí odkaz:
http://arxiv.org/abs/2303.18189
Autor:
Brinkman, Braden A. W.
The critical brain hypothesis posits that neural circuits may operate close to critical points of a phase transition, which has been argued to have functional benefits for neural computation. Theoretical and computational studies arguing for or again
Externí odkaz:
http://arxiv.org/abs/2301.09600
Autor:
Braden, H. W., Disney-Hogg, Linden
Publikováno v:
European Journal of Mathematics 10, 3 (2024)
Bring's curve, the unique Riemann surface of genus-4 with automorphism group $S_5$, has many exceptional properties. We review, give new proofs of, and extend a number of these including giving the complete realisation of the automorphism group for a
Externí odkaz:
http://arxiv.org/abs/2208.13692
We construct high rank solutions to Nahm's equations for boundary conditions that correspond to the Dirac multimonopole. Here, the spectral curve is explicitly known and we achieve the integration by constructing a basis of polynomial tuples that for
Externí odkaz:
http://arxiv.org/abs/2204.07822
Autor:
Brinkman, Braden A. W., Yan, Han, Maffei, Arianna, Park, Il Memming, Fontanini, Alfredo, Wang, Jin, La Camera, Giancarlo
Publikováno v:
Applied Physics Reviews (2022) 9(1), 011313
Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of patterns, which
Externí odkaz:
http://arxiv.org/abs/2110.03025
Autor:
Braden, H. W., Enolski, V. Z.
Recently we have shown how one may use use integrable systems techniques to implement the ADHMN construction and obtain general analytic formulae for the charge n su(2) Euclidean monopole. Here we do this for the case of charge 2: so answering an ope
Externí odkaz:
http://arxiv.org/abs/1903.00694