Diffuse Interstellar Bands Toward HD 62542

Diffuse interstellar bands (DIBs) have been detected for the first time along the peculiar translucent line of sight toward HD 62542, which passes through a diffuse cloud core. Although only a small fraction (18 out of more than 300) of generally weak DIB features have been shown to correlate with C_2 and C_3 (the "C_2 DIBs"), it is predominantly these DIBs that are observed toward HD 62542. The typically strong DIBs λλ5780 and 5797 are detected but are significantly weaker than toward other lines of sight with similar reddening. Other commonly observed DIBs (such as λλ4430, 6270, and 6284) remain noticeably absent. These observations further support the suggestion that the line of sight toward HD 62542 crosses only the core of a diffuse cloud and show that the correlation between the C_2 DIBs and small carbon chains is maintained in environments with very large fractions of molecular hydrogen, f_(H_2) > 0.8. A comparison of CH, CN, C_2, and C_3 column densities and C_2 DIB strengths toward HD 62542, HD 204827, and HD 172028 suggests that the line of sight toward HD 204827 passes through a diffuse cloud core similar to that seen toward HD 62542, as well as what might be referred to as a diffuse cloud envelope. This indicates that the bare core toward HD 62542 may not have significantly different relative chemical abundances from other diffuse cloud cores and that the C_2 DIBs may serve as a diagnostic of such cores

Observations of Rotationally Resolved C_3 in Translucent Sight Lines

The rotationally resolved spectrum of the A^1Π_u ← X^1Σ^+_g 000-000 transition of C_3, centered at 4051.6 Å, has been observed along 10 translucent lines of sight. To interpret these spectra, a new method for the determination of column densities and analysis of excitation profiles involving the simulation and fitting of observed spectra has been developed. The populations of lower rotational levels (J ≤ 14) in C_3 are best fitted by thermal distributions that are consistent with the kinetic temperatures determined from the excitation profile of C_2. Just as in the case of C_2, higher rotational levels (J > 14) of C_3 show increased nonthermal population distributions in clouds that have been determined to have total gas densities below ~500 cm^(-3)

Triangulations and a discrete Brunn-Minkowski inequality in the plane

For a set $A$ of points in the plane, not all collinear, we denote by ${\rm tr}(A)$ the number of triangles in any triangulation of $A$; that is, ${\rm tr}(A) = 2i+b-2$ where $b$ and $i$ are the numbers of points of $A$ in the boundary and the interior of $[A]$ (we use $[A]$ to denote "convex hull of $A$"). We conjecture the following analogue of the Brunn-Minkowski inequality: for any two point sets $A,B \subset {\mathbb R}^2$ one has $${\rm tr}(A+B)^{\frac12}\geq {\rm tr}(A)^{\frac12}+{\rm tr}(B)^{\frac12}.$$ We prove this conjecture in several cases: if $[A]=[B]$, if $B=A\cup\{b\}$, if $|B|=3$, or if none of $A$ or $B$ has interior points.Comment: 30 page

Contextuality and inductive bias in quantum machine learning

Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the types of data structures that lend themselves naturally to quantum models. In this work we look to quantum contextuality -- a form of nonclassicality with links to computational advantage -- for answers to this question. We introduce a framework for studying contextuality in machine learning, which leads us to a definition of what it means for a learning model to be contextual. From this, we connect a central concept of contextuality, called operational equivalence, to the ability of a model to encode a linearly conserved quantity in its label space. A consequence of this connection is that contextuality is tied to expressivity: contextual model classes that encode the inductive bias are generally more expressive than their noncontextual counterparts. To demonstrate this, we construct an explicit toy learning problem -- based on learning the payoff behaviour of a zero-sum game -- for which this is the case. By leveraging tools from geometric quantum machine learning, we then describe how to construct quantum learning models with the associated inductive bias, and show through our toy problem that they outperform their corresponding classical surrogate models. This suggests that understanding learning problems of this form may lead to useful insights about the power of quantum machine learning.Comment: comments welcom

Entanglement dynamics after a quench in Ising field theory: a branch point twist field approach

We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt ≫ 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)−3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points. © 2019, The Author(s)

SignaLink 2 - a signaling pathway resource with multi-layered regulatory networks.

BACKGROUND Signaling networks in eukaryotes are made up of upstream and downstream subnetworks. The upstream subnetwork contains the intertwined network of signaling pathways, while the downstream regulatory part contains transcription factors and their binding sites on the DNA as well as microRNAs and their mRNA targets. Currently, most signaling and regulatory databases contain only a subsection of this network, making comprehensive analyses highly time-consuming and dependent on specific data handling expertise. The need for detailed mapping of signaling systems is also supported by the fact that several drug development failures were caused by undiscovered cross-talk or regulatory effects of drug targets. We previously created a uniformly curated signaling pathway resource, SignaLink, to facilitate the analysis of pathway cross-talks. Here, we present SignaLink 2, which significantly extends the coverage and applications of its predecessor. DESCRIPTION We developed a novel concept to integrate and utilize different subsections (i.e., layers) of the signaling network. The multi-layered (onion-like) database structure is made up of signaling pathways, their pathway regulators (e.g., scaffold and endocytotic proteins) and modifier enzymes (e.g., phosphatases, ubiquitin ligases), as well as transcriptional and post-transcriptional regulators of all of these components. The user-friendly website allows the interactive exploration of how each signaling protein is regulated. The customizable download page enables the analysis of any user-specified part of the signaling network. Compared to other signaling resources, distinctive features of SignaLink 2 are the following: 1) it involves experimental data not only from humans but from two invertebrate model organisms, C. elegans and D. melanogaster; 2) combines manual curation with large-scale datasets; 3) provides confidence scores for each interaction; 4) operates a customizable download page with multiple file formats (e.g., BioPAX, Cytoscape, SBML). Non-profit users can access SignaLink 2 free of charge at http://SignaLink.org. CONCLUSIONS With SignaLink 2 as a single resource, users can effectively analyze signaling pathways, scaffold proteins, modifier enzymes, transcription factors and miRNAs that are important in the regulation of signaling processes. This integrated resource allows the systems-level examination of how cross-talks and signaling flow are regulated, as well as provide data for cross-species comparisons and drug discovery analyses