Faces of matrix models

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry prepotentials, as result of the action of W-operators and of various recursions on elementary input data, as gluing of certain elementary building blocks. All this explains the central role of such matrix models in modern mathematical physics: they provide the basic "special functions" to express the answers and relations between them, and they serve as a dream model of what one should try to achieve in any other field.Comment: 10 page

ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

General properties of multiparton webs: proofs from combinatorics

Recently, the diagrammatic description of soft-gluon exponentiation in scattering amplitudes has been generalized to the multiparton case. It was shown that the exponent of Wilson-line correlators is a sum of webs, where each web is formed through mixing between the kinematic factors and colour factors of a closed set of diagrams which are mutually related by permuting the gluon attachments to the Wilson lines. In this paper we use replica trick methods, as well as results from enumerative combinatorics, to prove that web mixing matrices are always: (a) idempotent, thus acting as projection operators; and (b) have zero sum rows: the elements in each row in these matrices sum up to zero, thus removing components that are symmetric under permutation of gluon attachments. Furthermore, in webs containing both planar and non-planar diagrams we show that the zero sum property holds separately for these two sets. The properties we establish here are completely general and form an important step in elucidating the structure of exponentiation in non-Abelian gauge theories.Comment: 38 pages, 10 figure

Webs in multiparton scattering using the replica trick

Soft gluon exponentiation in non-abelian gauge theories can be described in terms of webs. So far this description has been restricted to amplitudes with two hard partons, where webs were defined as the colour-connected subset of diagrams. Here we generalise the concept of webs to the multi-leg case, where the hard interaction involves non-trivial colour flow. Using the replica trick from statistical physics we solve the combinatorial problem of non-abelian exponentiation to all orders. In particular, we derive an algorithm for computing the colour factor associated with any given diagram in the exponent. The emerging result is exponentiation of a sum of webs, where each web is a linear combination of a subset of diagrams that are mutually related by permuting the eikonal gluon attachments to each hard parton. These linear combinations are responsible for partial cancellation of subdivergences, conforming with the renormalization of a multi-leg eikonal vertex. We also discuss the generalisation of exponentiation properties to beyond the eikonal approximatio

Palaeodemographic modelling supports a population bottleneck during the Pleistocene-Holocene transition in Iberia

Demographic change lies at the core of debates on genetic inheritance and resilience to climate change of prehistoric hunter-gatherers. Here we analyze the radiocarbon record of Iberia to reconstruct long-term changes in population levels and test different models of demographic growth during the Last Glacial-Interglacial transition. Our best fitting demographic model is composed of three phases. First, we document a regime of exponential population increase during the Late Glacial warming period (c.16.6-12.9 kya). Second, we identify a phase of sustained population contraction and stagnation, beginning with the cold episode of the Younger Dryas and continuing through the first half of the Early Holocene (12.9-10.2 kya). Finally, we report a third phase of density-dependent logistic growth (10.2-8 kya), with rapid population increase followed by stabilization. Our results support a population bottleneck hypothesis during the Last Glacial-Interglacial transition, providing a demographic context to interpret major shifts of prehistoric genetic groups in south-west Europe

Drugs in development for toxoplasmosis: advances, challenges, and current status

P Holland Alday,1 Joseph Stone Doggett1,2 1Division of Infectious Diseases, Oregon Health & Science University, 2Portland Veterans Affairs Medical Center, Portland, OR, USA Abstract: Toxoplasma gondii causes fatal and debilitating brain and eye diseases. Medicines that are currently used to treat toxoplasmosis commonly have toxic side effects and require prolonged courses that range from weeks to more than a year. The need for long treatment durations and the risk of relapsing disease are in part due to the lack of efficacy against T. gondii tissue cysts. The challenges for developing a more effective treatment for toxoplasmosis include decreasing toxicity, achieving therapeutic concentrations in the brain and eye, shortening duration, eliminating tissue cysts from the host, safety in pregnancy, and creating a formulation that is inexpensive and practical for use in resource-poor areas of the world. Over the last decade, significant progress has been made in identifying and developing new compounds for the treatment of toxoplasmosis. Unlike clinically used medicines that were repurposed for toxoplasmosis, these compounds have been optimized for efficacy against toxoplasmosis during preclinical development. Medicines with enhanced efficacy as well as features that address the unique aspects of toxoplasmosis have the potential to greatly improve toxoplasmosis therapy. This review discusses the facets of toxoplasmosis that are pertinent to drug design and the advances, challenges, and current status of preclinical drug research for toxoplasmosis. Keywords: Toxoplasma gondii, therapeutics, preclinical medicine, experimental medicine, mechanism of action, Apicomplex