Magnetic fields in Bok globules: Multi-wavelength polarimetry as tracer across large spatial scales

[abridged] The role of magnetic fields in the process of star formation is a matter of continuous debate. Clear observational proof of the general influence of magnetic fields on the early phase of cloud collapse is still pending. First results on Bok globules with simple structures indicate dominant magnetic fields across large spatial scales (Bertrang+2014). The aim of this study is to test the magnetic field influence across Bok globules with more complex density structures. We apply near-infrared polarimetry to trace the magnetic field structure on scales of 10^4-10^5au in selected Bok globules. The combination of these measurements with archival data in the optical and sub-mm wavelength range allows us to characterize the magnetic field on scales of 10^3-10^6au. We present polarimetric data in the near-infrared wavelength range for the three Bok globules CB34, CB56, and [OMK2002]18, combined with archival polarimetric data in the optical wavelength range for CB34 and CB56, and in the sub-millimeter wavelength range for CB34 and [OMK2002]18. We find a strong polarization signal (P>2%) in the near-infrared and strongly aligned polarization segments on large scales (10^4-10^6au) for all three globules. This indicates dominant magnetic fields across Bok globules with complex density structures. To reconcile our findings in globules, the lowest mass clouds known, and the results on intermediate (e.g., Taurus) and more massive (e.g., Orion) clouds, we postulate a mass dependent role of magnetic fields, whereby magnetic fields appear to be dominant on low and high mass but rather sub-dominant on intermediate mass clouds.Comment: 7 pages, 6 figures; Accepted by A&

On a conjecture of Brouwer involving the connectivity of strongly regular graphs

In this paper, we study a conjecture of Andries E. Brouwer from 1996 regarding the minimum number of vertices of a strongly regular graph whose removal disconnects the graph into non-singleton components. We show that strongly regular graphs constructed from copolar spaces and from the more general spaces called $\Delta$-spaces are counterexamples to Brouwer's Conjecture. Using J.I. Hall's characterization of finite reduced copolar spaces, we find that the triangular graphs $T(m)$, the symplectic graphs $Sp(2r,q)$ over the field $\mathbb{F}_q$ (for any $q$ prime power), and the strongly regular graphs constructed from the hyperbolic quadrics $O^{+}(2r,2)$ and from the elliptic quadrics $O^{-}(2r,2)$ over the field $\mathbb{F}_2$, respectively, are counterexamples to Brouwer's Conjecture. For each of these graphs, we determine precisely the minimum number of vertices whose removal disconnects the graph into non-singleton components. While we are not aware of an analogue of Hall's characterization theorem for $\Delta$-spaces, we show that complements of the point graphs of certain finite generalized quadrangles are point graphs of $\Delta$-spaces and thus, yield other counterexamples to Brouwer's Conjecture. We prove that Brouwer's Conjecture is true for many families of strongly regular graphs including the conference graphs, the generalized quadrangles $GQ(q,q)$ graphs, the lattice graphs, the Latin square graphs, the strongly regular graphs with smallest eigenvalue -2 (except the triangular graphs) and the primitive strongly regular graphs with at most 30 vertices except for few cases. We leave as an open problem determining the best general lower bound for the minimum size of a disconnecting set of vertices of a strongly regular graph, whose removal disconnects the graph into non-singleton components.Comment: 25 pages, 1 table; accepted to JCTA; revised version contains a new section on copolar and Delta space

The chromatic index of strongly regular graphs

We determine (partly by computer search) the chromatic index (edge-chromatic number) of many strongly regular graphs (SRGs), including the SRGs of degree $k \leq 18$ and their complements, the Latin square graphs and their complements, and the triangular graphs and their complements. Moreover, using a recent result of Ferber and Jain it is shown that an SRG of even order $n$, which is not the block graph of a Steiner 2-design or its complement, has chromatic index $k$, when $n$ is big enough. Except for the Petersen graph, all investigated connected SRGs of even order have chromatic index equal to their degree, i.e., they are class 1, and we conjecture that this is the case for all connected SRGs of even order.Comment: 10 page

Disconnecting strongly regular graphs

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner $2$-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency

The graphs with all but two eigenvalues equal to −2-2 or 00

We determine all graphs for which the adjacency matrix has at most two eigenvalues (multiplicities included) not equal to $-2$, or $0$, and determine which of these graphs are determined by their adjacency spectrum

Optimal evaluation of single-molecule force spectroscopy experiments

The forced rupture of single chemical bonds under external load is addressed. A general framework is put forward to optimally utilize the experimentally observed rupture force data for estimating the parameters of a theoretical model. As an application we explore to what extent a distinction between several recently proposed models is feasible on the basis of realistic experimental data sets.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.

Volume Dependence of Bound States with Angular Momentum

We derive general results for the mass shift of bound states with angular momentum l >= 1 in a finite periodic volume. Our results have direct applications to lattice simulations of hadronic molecules as well as atomic nuclei. While the binding of S-wave bound states increases at finite volume, we show that the binding of P-wave bound states decreases. The mass shift for D-wave bound states as well as higher partial waves depends on the representation of the cubic rotation group. Nevertheless, the multiplet-averaged mass shift for any angular momentum l can be expressed in a simple form, and the sign of the shift alternates for even and odd l. We verify our analytical results with explicit numerical calculations. We also show numerically that similar volume corrections appear in three-body bound states.Comment: 4 pages, 3 figures, final versio

Inferring decoding strategy from choice probabilities in the presence of noise correlations

The activity of cortical neurons in sensory areas covaries with perceptual decisions, a relationship often quantified by choice probabilities. While choice probabilities have been measured extensively, their interpretation has remained fraught with difficulty. Here, we derive the mathematical relationship between choice probabilities, read-out weights and noise correlations within the standard neural decision making model. Our solution allows us to prove and generalize earlier observations based on numerical simulations, and to derive novel predictions. Importantly, we show how the read-out weight profile, or decoding strategy, can be inferred from experimentally measurable quantities. Furthermore, we present a test to decide whether the decoding weights of individual neurons are optimal, even without knowing the underlying noise correlations. We confirm the practical feasibility of our approach using simulated data from a realistic population model. Our work thus provides the theoretical foundation for a growing body of experimental results on choice probabilities and correlations