An analogue of Ryser's Theorem for partial Sudoku squares

In 1956 Ryser gave a necessary and sufficient condition for a partial latin rectangle to be completable to a latin square. In 1990 Hilton and Johnson showed that Ryser's condition could be reformulated in terms of Hall's Condition for partial latin squares. Thus Ryser's Theorem can be interpreted as saying that any partial latin rectangle $R$ can be completed if and only if $R$ satisfies Hall's Condition for partial latin squares. We define Hall's Condition for partial Sudoku squares and show that Hall's Condition for partial Sudoku squares gives a criterion for the completion of partial Sudoku rectangles that is both necessary and sufficient. In the particular case where $n=pq$, $p|r$, $q|s$, the result is especially simple, as we show that any $r \times s$ partial $(p,q)$-Sudoku rectangle can be completed (no further condition being necessary).Comment: 19 pages, 10 figure

Recovering refined surface normals for relighting clothing in dynamic scenes

In this paper we present a method to relight captured 3D video sequences of non-rigid, dynamic scenes, such as clothing of real actors, reconstructed from multiple view video. A view-dependent approach is introduced to refine an initial coarse surface reconstruction using shape-from-shading to estimate detailed surface normals. The prior surface approximation is used to constrain the simultaneous estimation of surface normals and scene illumination, under the assumption of Lambertian surface reflectance. This approach enables detailed surface normals of a moving non-rigid object to be estimated from a single image frame. Refined normal estimates from multiple views are integrated into a single surface normal map. This approach allows highly non-rigid surfaces, such as creases in clothing, to be relit whilst preserving the detailed dynamics observed in video

The nuclear scissors mode within two approaches (Wigner function moments versus RPA)

Two complementary methods to describe the collective motion, RPA and Wigner function moments method, are compared on an example of a simple model - harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model including the scissors mode, which here is the subject of our special attention. The exact relation between the variables of the two methods and the respective dynamical equations is established. The normalization factor of the "synthetic" scissors state and its overlap with physical states are calculated analytically. The orthogonality of the spurious state to all physical states is proved rigorously.Comment: 39 page

Generalised Moore spectra in a triangulated category

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we obtain a functor which "approximates" objects of the module category of the endomorphism algebra of C in T. This generalises and extends a construction of Jorgensen in connection with lifts of certain homological functors of derived categories. We show that this new functor is well-behaved with respect to short exact sequences and distinguished triangles, and as a consequence we obtain a new way of embedding the module category in a triangulated category. As an example of the theory, we recover Keller's canonical embedding of the module category of a path algebra of a quiver with no oriented cycles into its u-cluster category for u>1.Comment: 26 pages, improvement to exposition of the proof of Theorem 3.

Softening of the insulating phase near Tc for the photo-induced insulator-to-metal phase transition in vanadium dioxide

We use optical-pump terahertz-probe spectroscopy to investigate the near-threshold behavior of the photoinduced insulator-to-metal (IM) transition in vanadium dioxide thin films. Upon approaching Tc a reduction in the fluence required to drive the IM transition is observed, consistent with a softening of the insulating state due to an increasing metallic volume fraction (below the percolation limit). This phase coexistence facilitates the growth of a homogeneous metallic conducting phase following superheating via photoexcitation. A simple dynamic model using Bruggeman effective medium theory describes the observed initial condition sensitivity.Comment: accepted for publication in Physical Review Letter