Strong coupling from the Hubbard model

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter \lambda becomes large. We show that the full dimension \Delta of the Konishi superpartner is the solution of a sixth order polynomial while \Delta for a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large \lambda and the equations can be inverted to express \lambda as an explicit function of \Delta. We then consider more general operators and show how \Delta depends on \lambda in the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of \lambda. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.Comment: 14 pages; v2: 17 pages, 2 figures, appendix and references added; typos fixed, minor changes; v3 fixed figures; v4 more references added, minor correctio

Computations in Large N Matrix Mechanics

The algebraic formulation of Large N matrix mechanics recently developed by Halpern and Schwartz leads to a practical method of numerical computation for both action and Hamiltonian problems. The new technique posits a boundary condition on the planar connected parts X_w, namely that they should decrease rapidly with increasing order. This leads to algebraic/variational schemes of computation which show remarkably rapid convergence in numerical tests on some many- matrix models. The method allows the calculation of all moments of the ground state, in a sequence of approximations, and excited states can be determined as well. There are two unexpected findings: a large d expansion and a new selection rule for certain types of interaction.Comment: 27 page

Odor Detection in Manduca sexta Is Optimized when Odor Stimuli Are Pulsed at a Frequency Matching the Wing Beat during Flight

Sensory systems sample the external world actively, within the context of self-motion induced disturbances. Mammals sample olfactory cues within the context of respiratory cycles and have adapted to process olfactory information within the time frame of a single sniff cycle. In plume tracking insects, it remains unknown whether olfactory processing is adapted to wing beating, which causes similar physical effects as sniffing. To explore this we first characterized the physical properties of our odor delivery system using hotwire anemometry and photo ionization detection, which confirmed that odor stimuli were temporally structured. Electroantennograms confirmed that pulse trains were tracked physiologically. Next, we quantified odor detection in moths in a series of psychophysical experiments to determine whether pulsing odor affected acuity. Moths were first conditioned to respond to a target odorant using Pavlovian olfactory conditioning. At 24 and 48 h after conditioning, moths were tested with a dilution series of the conditioned odor. On separate days odor was presented either continuously or as 20 Hz pulse trains to simulate wing beating effects. We varied pulse train duty cycle, olfactometer outflow velocity, pulsing method, and odor. Results of these studies, established that detection was enhanced when odors were pulsed. Higher velocity and briefer pulses also enhanced detection. Post hoc analysis indicated enhanced detection was the result of a significantly lower behavioral response to blank stimuli when presented as pulse trains. Since blank responses are a measure of false positive responses, this suggests that the olfactory system makes fewer errors (i.e. is more reliable) when odors are experienced as pulse trains. We therefore postulate that the olfactory system of Manduca sexta may have evolved mechanisms to enhance odor detection during flight, where the effects of wing beating represent the norm. This system may even exploit temporal structure in a manner similar to sniffing

Loop Space Hamiltonians And Field Theory Of Non-Critical Strings

We consider the loop space representation of multi-matrix models. Explaining the origin of a time variable through stochastic quantization we make contact with recent proposals of Ishibashi and Kawai. We demonstrate how collective field theory with its loop space interactions generates a field theory of non-critical strings.Comment: 23 pages; phyzztex; Misprints corrected and Tex fonts adde

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Giant Magnons and Singular Curves

We obtain the giant magnon of Hofman-Maldacena and its dyonic generalisation on R x S^3 < AdS_5 x S^5 from the general elliptic finite-gap solution by degenerating its elliptic spectral curve into a singular curve. This alternate description of giant magnons as finite-gap solutions associated to singular curves is related through a symplectic transformation to their already established description in terms of condensate cuts developed in hep-th/0606145.Comment: 34 pages, 17 figures, minor change in abstrac

Geodesic Distance in Planar Graphs

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated trees, leading to a recursion relation on the geodesic distance. The latter is solved exactly in terms of discrete soliton-like expressions, suggesting an underlying integrable structure. We extract from this solution the fractal dimensions at the various (multi)-critical points, as well as the precise scaling forms of the continuum two-point functions and the probability distributions for the geodesic distance in (multi)-critical random surfaces. The two-point functions are shown to obey differential equations involving the residues of the KdV hierarchy.Comment: 38 pages, 8 figures, tex, harvmac, eps

Chemotherapy following radium-223 dichloride treatment in ALSYMPCA

BACKGROUND Radium-223 prolongs overall survival in patients with castration-resistant prostate cancer (CRPC) and symptomatic bone metastases, regardless of prior docetaxel. Whether or not chemotherapy can be safely administered following radium-223 treatment is of clinical importance. An exploratory analysis of prospectively collected data, from the ALSYMPCA (ALpharadin in SYMptomatic Prostate CAncer) patient subgroup who received chemotherapy after radium-223 or placebo treatment, was conducted to evaluate the safety and efficacy of chemotherapy following radium-223. METHODS In ALSYMPCA, CRPC patients with symptomatic bone metastases and no visceral metastases were randomized 2:1 to receive six injections of radium-223 (50 kBq/kg IV) or placebo plus best standard of care, stratified by prior docetaxel, baseline alkaline phosphatase, and current bisphosphonate use. In this exploratory analysis, chemotherapy agents administered following study treatment were identified; timing and duration were calculated. Hematologic safety was reviewed, and overall survival analyzed. RESULTS Overall, 142 radium-223 and 64 placebo patients received subsequent chemotherapy; most common were docetaxel (70% radium-223, 72% placebo) and mitoxantrone (16% radium-223, 20% placebo). The majority of patients (61% radium-223, 58% placebo) had received prior docetaxel. Radium-223 patients started subsequent chemotherapy later than placebo patients; chemotherapy duration was similar between groups. In radium-223 and placebo patients receiving subsequent chemotherapy, median hematologic values (hemoglobin, neutrophils, and platelets) remained nearly constant up to 18 months following start of chemotherapy, regardless of prior docetaxel treatment. A low percentage of patients in both groups had grades 3–4 hematologic values (<10%). Platelet count decline, from last measurement before chemotherapy, was numerically greater in radium-223 versus placebo patients. Median overall survivals from start of chemotherapy were 16.0 and 15.8 months following radium-223 and placebo, respectively. CONCLUSIONS Chemotherapy following radium-223, regardless of prior docetaxel, is feasible and appears to be well tolerated in patients with CRPC and symptomatic bone metastases