Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system Dn (the classical theorem corresponds to the An-case). Several byproducts of the developed technique, such as a new formula for a specialization of the multivariate Tutte polynom...

Few weed species have gained so much attention over the past decade as waterhemp. Waterhemp has gone from an obscure weed species in the 1980s to a species that has achieved widespread distinction throughout most of the Midwest. This species gained its notoriety in the early 1990s when it began appearing in many corn and soybean fields in Illinois, Iowa, Kansas, and Missouri. In these fields AL...

The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained by prohibiting the specification of prefixes or suffixes. As it turns out, these language classes are in one-to-one correspondence with fragments of existen...

These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a n×n random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex plane as the dimension n tends to infinity. This phenomenon is the non-Hermitian counterpart of the semi circular limit for Wigner random Hermitian matrices, ...

The red flour beetle, Tribolium castaneum, has been selected for whole genome shotgun sequencing in the next year. In this minireview, we discuss some of the genetic and genomic tools and biological properties of Tribolium that have established its importance as an organism for agricultural and biomedical research as well as for studies of development and evolution. A Tribolium genomic database...

icrotubule (MT) assembly is a dynamic process involving the addition and removal of tubulin ␣␤ heterodimers. The binding of microtubule-associated proteins (MAPs) to MTs helps to prevent depolymerization M of assembled filaments. Despite years of study, there has been little consensus on the structural basis for this stabilization. Open a number of textbooks on the subject, and you are likely t...

In traditional video, the user is locked to the angle where the camera was pointing to during the capture of the video. With 360o video recording, there are no longer these boundaries, and 360o video capturing devices are becoming more common and affordable to the general public. Hypervideo stretches boundaries even further, allowing to explore the video and to navigate to related information. ...

We present ISOCAM 7 µm and 15 µm observations of 12 nearby white dwarfs, 6 of which have been found to have metals such as Ca, Mg and Fe in their pho-tospheres. Our purpose was to search for an excess of infrared emission above the stellar photospheres. We find that none of the white dwarfs other than G29−38 shows a detectable infrared excess and this places strong constraints on the existence ...

We analyze quasi-topological solitons winding around a mexican-hat potential in two space-time dimensions. They are prototypes for a large number of physical excitations, including Skyrmions of the Higgs sector of the standard electroweak model, magnetic bubbles in thin ferromagnetic films, and strings in certain non-trivial backgrounds. We present explicit solutions, derive the conditions for ...