Sinks in Acyclic Orientations of Graphs

Greene and Zaslavsky proved that the number of acyclic orientations of a graph with a unique sink is, up to sign, the linear coefficient of the chromatic polynomial. We give three new proofs of this result using pure induction, noncommutative symmetric functions, and an algorithmic bijection.Comment: 17 pages, 1 figur

Comparison of Variational Approaches for the Exactly Solvable 1/r-Hubbard Chain

We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional $1/r$-Hubbard model. We find that none of these variational wave functions is able to correctly reproduce the physics of the metal-to-insulator transition which occurs in the model for half-filled bands when the interaction strength equals the bandwidth. The many-particle problem to calculate the variational ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave function is exactly solved for the~$1/r$-Hubbard model. The latter wave function becomes exact both for small and large interaction strength, but it incorrectly predicts the metal-to-insulator transition to happen at infinitely strong interactions. We conclude that neither Hartree-Fock nor Jastrow-type wave functions yield reliable predictions on zero temperature phase transitions in low-dimensional, i.e., charge-spin separated systems.Comment: 23 pages + 3 figures available on request; LaTeX under REVTeX 3.

Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model

For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the Density-Matrix Renormalization Group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the band width. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approaches. In Wannier theory, we perturb the Wannier exciton states to second order. In two-step perturbation theory, similar in spirit to the GW-BSE approach, we form excitons from dressed electron-hole excitations. We find the Wannier approach to be superior to the two-step perturbation theory. For singlet excitons, Wannier theory is applicable up to Coulomb parameters as large as half band width. For triplet excitons, second-order perturbation theory quickly fails completely.Comment: 32 pages, 12 figures, submtted to JSTA

Ground-state phase diagram of a half-filled one-dimensional extended Hubbard model

The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion, and hopping t. A critical line V_c(U) approximately equal to U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V > 2t changes the phase transition from continuous to first order at a tricritical point U_t = 3.7t, V_t=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V_c(U) for U_t < U < 7-8 t.Comment: 4 pages (REVTEX 4), 3 EPS figures, shorter abstract, text and references modifie

Convolutional neural networks: a magic bullet for gravitational-wave detection?

In the last few years, machine learning techniques, in particular convolutional neural networks, have been investigated as a method to replace or complement traditional matched filtering techniques that are used to detect the gravitational-wave signature of merging black holes. However, to date, these methods have not yet been successfully applied to the analysis of long stretches of data recorded by the Advanced LIGO and Virgo gravitational-wave observatories. In this work, we critically examine the use of convolutional neural networks as a tool to search for merging black holes. We identify the strengths and limitations of this approach, highlight some common pitfalls in translating between machine learning and gravitational-wave astronomy, and discuss the interdisciplinary challenges. In particular, we explain in detail why convolutional neural networks alone cannot be used to claim a statistically significant gravitational-wave detection. However, we demonstrate how they can still be used to rapidly flag the times of potential signals in the data for a more detailed follow-up. Our convolutional neural network architecture as well as the proposed performance metrics are better suited for this task than a standard binary classifications scheme. A detailed evaluation of our approach on Advanced LIGO data demonstrates the potential of such systems as trigger generators. Finally, we sound a note of caution by constructing adversarial examples, which showcase interesting "failure modes" of our model, where inputs with no visible resemblance to real gravitational-wave signals are identified as such by the network with high confidence.Comment: First two authors contributed equally; appeared at Phys. Rev.

The in vivo interaction of Streptococcal mAb10F5 in Lewis rat brains : an honors thesis (HONRS 499)

Group A streptococcal infection is being implicated in the formation of movement disorders such as PANDAS, Tourette syndrome, Sydenham's chorea, and general tics. It is suggested that antibodies produced against the conservative region of streptococcal M proteins are cross-reacting with neuronal tissue in an autoimmune response. One area of proposed cross-reactivity within the brain is the basal ganglia, the center for movement regulation. Antibodies against this region are called anti-basal ganglia antibodies. Monoclonal mouse antibody 10F5 (mAb10F5) is a streptococcal M6 antibody. Previous studies in our laboratory, using in vitro techniques, demonstrated that mAb10F5 bound in the basal ganglia of Lewis rats and has antiphospholipid properties. The current study sought to examine the interaction of mAb10F5 in Lewis rat brains in vivo. Rats were injected with either mAb10F5 or a positive control, myosin (type II) antibody, and euthanized after 24, 48, or 72 hours. Slices from the rostral and midrostral sections of these brains along with those of uninjected controls were analyzed using immunofluorescence and fluorescent microscopy. The caudate and putamen (CPu), a part of the basal ganglia, was significantly positive compared to controls at 24, 48, and 72 hours in the mAb10F5 treated group and at 24 and 48 hours in the myosin (type II) antibody treated group. It was discerned that in the mAb10F5 group the antibody crossed the blood-brain-barrier at 24 hours and remained in the CPu through 72 hours. The myosin (type II) antibody did not cross the blood-brain-barrier until 48 hours, and was no longer significantly in the CPu after 72 hours. These findings suggest that mAb10F5 is an anti-basal ganglia antibody and may be involved in movement disorders.Honors CollegeThesis (B.?.

Mott-Hubbard transition in infinite dimensions

We calculate the zero-temperature gap and quasiparticle weight of the half-filled Hubbard model with a random dispersion relation. After extrapolation to the thermodynamic limit, we obtain reliable bounds on these quantities for the Hubbard model in infinite dimensions. Our data indicate that the Mott-Hubbard transition is continuous, i.e., that the quasiparticle weight becomes zero at the same critical interaction strength at which the gap opens.Comment: 4 pages, RevTeX, 5 figures included with epsfig Final version for PRL, includes L=14 dat