On Elliptical Billiards in the Lobachevsky Space and associated Geodesic Hierarchies

We derive Cayley's type conditions for periodical trajectories for the billiard within an ellipsoid in the Lobachevsky space. It appears that these new conditions are of the same form as those obtained before for the Euclidean case. We explain this coincidence by using theory of geodesically equivalent metrics and show that Lobachevsky and Euclidean elliptic billiards can be naturally considered as a part of a hierarchy of integrable elliptical billiards.Comment: 14 pages, to appear in Journal of Geometry and Physic

Inherited crustal deformation along the East Gondwana margin revealed by seismic anisotropy tomography

Acknowledgments We thank Mallory Young for providing phase velocity measurements in mainland Australia and Tasmania. Robert Musgrave is thanked for making available his tilt-filtered magnetic intensity map. In the short term, data may be made available by contacting the authors (S.P. or N.R.). A new database of passive seismic data recorded in Australia is planned as part of a national geophysics data facility for easy access download. Details on the status of this database may be obtained from the authors (S.P., N.R., or A.M.R.). There are no restrictions on access for noncommercial use. Commercial users should seek written permission from the authors (S.P. or N.R.). Ross Cayley publishes with the permission of the Director of the Geological Survey of Victoria.Peer reviewedPublisher PD

A three-qubit interpretation of BPS and non-BPS STU black holes

Following the recent trend we develop further the black hole analogy between quantum information theory and the theory of extremal stringy black hole solutions. We show that the three-qubit interpretation of supersymmetric black hole solutions in the STU model can be extended also to include non-supersymmetric ones. First we show that the black hole potential can be expressed as one half the norm of a suitably chosen three-qubit entangled state containing the quantized charges and the moduli. The extremization of the black hole potential in terms of this entangled state amounts to either supressing bit flip errors (BPS-case) or allowing very special types of flips transforming the states between different classes of non-BPS solutions. We are illustrating our results for the example of the D2-D6 system. In this case the bit flip errors are corresponding to sign flip errors of the charges originating from the number of D2 branes. After moduli stabilization the states depending entirely on the charges are maximally entangled graph states (of the triangle graph) well-known from quantum information theory. An N=8 interpretation of the STU-model in terms of a mixed state with fermionic purifications is also given.Comment: 35 page

Writer's block is not a struggle with your writing but with your thinking. Write your way out of it

Most graduate writers who are struggling with their writing are actually struggling with their thinking. It isn't a psychological block, but rather the intellectual confusions endemic to the process of communicating sophisticated research. To Rachael Cayley, these confusions are real and can have deleterious consequences for writing, but when we treat these problems as conceptual problems in our thinking we create the space to use writing as a strategy to solve them. The writer’s block label may just be further alienating us from our own writing; write your way out

Equation of state of low--density neutron matter and the 1S0^1S_0 pairing gap

We report results of the equation of state of neutron matter in the low--density regime, where the Fermi wave vector ranges from $0.4 fm^{-1} \leq k_F \leq 1.0 fm^{-1}$. Neutron matter in this regime is superfluid because of the strong and attractive interaction in the $^1S_0$ channel. The properties of this superfluid matter are calculated starting from a realistic Hamiltonian that contains modern two-- and three--body interactions. The ground state energy and the $^1S_0$ superfluid energy gap are calculated using the Auxiliary Field Diffusion Monte Carlo method. We study the structure of the ground state by looking at pair distribution functions as well as the Cooper-pair wave function used in the calculations.Comment: 12 pages, 7 figure

A Generalized Enumeration of Labeled Trees and Reverse Pr\"ufer Algorithm

A {\em leader} of a tree $T$ on $[n]$ is a vertex which has no smaller descendants in $T$. Gessel and Seo showed \sum_{T \in \mathcal{T}_n}u^\text{(# of leaders in $T$)} c^\text{(degree of 1 in $T$)}=u P_{n-1}(1,u,cu), which is a generalization of Cayley formula, where $\mathcal{T}_n$ is the set of trees on $[n]$ and $$P_n(a,b,c)=c\prod_{i=1}^{n-1}(ia+(n-i)b+c).$$ Using a variation of Pr\"ufer code which is called a {\em RP-code}, we give a simple bijective proof of Gessel and Seo's formula.Comment: 5 pages, 3 figure

Between Manuscript and Print: Literary Reception in Late Medieval France

The final publication is available at Springer via http://dx.doi.org/10.1007/s40647-015-0067-xBased on original archival and codicological research, this paper investigates the transformations and negotiations between manuscript and printed versions of fifteenth-century poetry through the specific example of one surprisingly complex debate poem, Le Songe de la Pucelle (The Dream of the Virgin). Our debate relates the choice that a female narrator must make between the respective appeals of two personifications, Love and Shame, who appear to her in a dream-vision. The manuscript tradition invariably collects the poem with other fifteenth-century debates and moral texts, while the early printed copies tended to have experienced a prior separate circulation and often remain as monotextual pamphlets. Manuscript and printed copies of the same poem seem, then, to target different audiences. My paper investigates this curious divergence in the transmission pattern of the manuscript and printed versions of the Songe and seeks possible answers in the very different sets of images accompanying the text in manuscript and printed versions