We present a model based on the concept of saturation for small $Q^2$ and small $x$. With only three parameters we achieve a good description of all Deep Inelastic Scattering data below $x=0.01$. This includes a consistent treatment of charm and a successful extrapolation into the photoproduction regime. The same model leads to a roughly constant ratio of diffractive and inclusive cross section.
Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.
A bstractWe introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous global symmetry leads to constructions that involve solving ODEs instead of PDEs. We study in detail D = 4 Einstein-Maxwell theory coupled to a complex scalar field with a simple mass term. We construct black holes dual to metallic phases which exhibit a Drude-type peak in the optical conductivity, but there is no evidence of an intermediate scaling that has been reported in other holographic lattice constructions. We also construct black holes dual to insulating phases which exhibit a suppression of spectral weight at low frequencies. We show that the model also admits a novel AdS3 × $ \mathbb{R} $ solution.
Luis A. Álvarez-García, Wolfram Liebermeister, Ian Leifer
et al.
Symmetry principles play an important role in geometry, and physics, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems are often highly complex and may consist of a large number of interacting parts. Using symmetry fibrations, the relevant symmetries for biological "message-passing" networks, we introduce a scheme, called Complexity Reduction by Symmetry or ComSym, to reduce the gene regulatory networks of Escherichia coli and Bacillus subtilis bacteria to core networks in a way that preserves the dynamics and uncovers the computational capabilities of the network. Gene nodes in the original network that share isomorphic input trees are collapsed by the fibration into equivalence classes called fibers, whereby nodes that receive signals with the same "history" belong to one fiber and synchronize. Then we reduce the networks to its minimal computational core via k-core decomposition. This computational core consists of a few strongly connected components or "signal vortices", in which signals can cycle through. While between them, these "signal vortices" transmit signals in a feedforward manner. These connected components perform signal processing and decision making in the bacterial cell by employing a series of genetic toggle-switch circuits that store memory, plus oscillator circuits. These circuits act as the central computation device of the network, whose output signals then spread to the rest of the network. Our reduction method opens the door to narrow the vast complexity of biological systems to their minimal parts in a systematic way by using fundamental theoretical principles of symmetry.
The exterior gravitational field of a slowly-rotating neutron star can be characterized by its multipole moments, the first few being the neutron star mass, moment of inertia, and quadrupole moment to quadratic order in spin. In principle, all of these quantities depend on the neutron star's internal structure, and thus, on unknown nuclear physics at supra-nuclear energy densities. We here find relations between the moment of inertia, the Love numbers and the quadrupole moment (I-Love-Q relations) that do not depend sensitively on the neutron star's internal structure. Three important consequences derive from these I-Love-Q relations. On an observational astrophysics front, the measurement of a single member of the I-Love-Q trio would automatically provide information about the other two, even when the latter may not be observationally accessible. On a gravitational wave front, the I-Love-Q relations break the degeneracy between the quadrupole moment and the neutron-star spins in binary inspiral waveforms, allowing second-generation ground-based detectors to determine the (dimensionless) averaged spin to $\mathcal{O}(10)%$, given a sufficiently large signal-to-noise ratio detection. On a fundamental physics front, the I-Love-Q relations allow for tests of General Relativity in the neutron-star strong-field that are both theory- and internal structure-independent. As an example, by combining gravitational-wave and electromagnetic observations, one may constrain dynamical Chern-Simons gravity in the future by more than 6 orders of magnitude more stringently than Solar System and table-top constraints.
We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by Guo. We also deduce a $q$-analogue of a congruence due to Apagodu and Zeilberger from Guo's $q$-congruence.
Rafael Arturo Torres-Fajardo, Pedro Geraldo González-Pech, Juan Felipe de Jesús Torres-Acosta
et al.
Nutraceuticals are defined as livestock feeds that combine their nutritional value with their beneficial effects on animal health. We analyzed the outcomes from nearly 20 years of research assessing the nutraceutical properties of plants consumed by sheep and goats in low deciduous forests. A systematic review of different databases suggested 31 peer-reviewed manuscripts according to pre-established criteria. Amongst these, 16 manuscripts described in vitro evaluations investigating the bioactivity of plant secondary compounds in the extracts of 12 plant species. Most of these studies used the abomasal nematode Haemonchus contortus as the parasite model. Meanwhile, 11 manuscripts reported in vivo trials under controlled pen conditions, evaluating the relationships between the intake of leaves from different plant species and their secondary compounds and animal nutrition, performance, and gastrointestinal nematode infections. Additionally, four manuscripts described studies under natural feeding conditions. Altogether, the studies showed the inherent complexity of the relationship between small ruminants, plants, nutrients, secondary compounds, and gastrointestinal nematodes in natural feeding systems. Several plant species can be considered good candidates for nutraceutical use. Our findings warrant future work to understand the relationship between plants, ruminants, and their parasites, with the aim to improve the sustainability of production systems based on the native vegetation of tropical forests.
We demonstrate that ideal anapole metamaterials have infinite Q-factor. We have designed and fabricated a metamaterial consisting of planar metamolecules which exhibit anapole behavior in the sense that the electric dipole radiation is almost cancelled by the toroidal dipole one, producing thus an extremely high Q-factor at the resonance frequency. The size of the system, at the mm range, and the parasitic magnetic quadrupole radiation are the factors limiting the size of the Q-factor. In spite of the very low radiation losses the local fields at the metamolecules are extremely high, of the order of higher than the external incoming field.
We introduce new classes of q -starlike and q -convex functions of complex order involving the q -derivative operator defined in the open unit disc. Furthermore, we find estimates on the coefficients for second and third coefficients of these classes. Mathematics subject classification (2010): Primary 30C45; Secondary 30C80.