Sensitivity of Evapotranspiration Models to Onsite and Offsite Meteorological Data for a Ponderosa Pine Forest

Evapotranspiration (ET) is a major component of the water budget in most forests, in many cases exceeding 70% of annual precipitation. Due to limitations in time and resources, input data necessary to model ET are not always available for a study site, but offsite data from meteorological networks may be a suitable substitute. In this study, we evaluated three models for estimating ET, Priestly-Taylor (P-T), Shuttleworth-Wallace (S-W), and Penman-Monteith with dynamic stomatal resistance (P-M-d), in a ponderosa pine (Pinus ponderosa) forest in northern Arizona where eddy covariance data exist for comparison. We tested the sensitivity of the models to the use of offsite meteorological data from a weather station and offsite soil moisture data from two snow monitoring sites in the SNOTEL network. Onsite data are required for accurate ET estimation with the P-M-d model because of its complexity. Acceptable accuracy in ET estimation required onsite net radiation data for the P-T model and onsite vapor pressure deficit data for the S-W model; other input data can be obtained from nearby offsite weather stations. Errors in ET estimation produced by the use of offsite soil moisture data varied between two nearby SNOTEL sites. Recommendations about the use of offsite data are presented

Sparse Deterministic Approximation of Bayesian Inverse Problems

We present a parametric deterministic formulation of Bayesian inverse problems with input parameter from infinite dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial differential equations, and the inverse problem is to determine the unknown, parametric deterministic coefficients from noisy observations comprising linear functionals of the solution. We prove a generalized polynomial chaos representation of the posterior density with respect to the prior measure, given noisy observational data. We analyze the sparsity of the posterior density in terms of the summability of the input data's coefficient sequence. To this end, we estimate the fluctuations in the prior. We exhibit sufficient conditions on the prior model in order for approximations of the posterior density to converge at a given algebraic rate, in terms of the number $N$ of unknowns appearing in the parameteric representation of the prior measure. Similar sparsity and approximation results are also exhibited for the solution and covariance of the elliptic partial differential equation under the posterior. These results then form the basis for efficient uncertainty quantification, in the presence of data with noise

Treatment-resistant pediatric giant prolactinoma and multiple endocrine neoplasia type 1

Background Pediatric pituitary adenomas are rare, accounting for <3 % of all childhood intracranial tumors, the majority of which are prolactinomas. Consequently, they are often misdiagnosed as other suprasellar masses such as craniopharyngiomas in this age group. Whilst guidelines exist for the treatment of adult prolactinomas, the management of childhood presentations of these benign tumors is less clear, particularly when dopamine agonist therapy fails. Given their rarity, childhood-onset pituitary adenomas are more likely to be associated with a variety of genetic syndromes, the commonest being multiple endocrine neoplasia type 1 (MEN-1). Case description We present a case of an early-onset, treatment-resistant giant prolactinoma occurring in an 11-year-old peripubertal boy that was initially sensitive, but subsequently highly resistant to dopamine agonist therapy, ultimately requiring multiple surgical debulking procedures and proton beam irradiation. Our patient is now left with long-term tumor- and treatment-related neuroendocrine morbidities including blindness and panhypopituitarism. Only after multiple consultations and clinical data gained from 20-year-old medical records was a complex, intergenerationally consanguineous family history revealed, compatible with MEN-1, with a splice site mutation (c.784-9G > A) being eventually identified in intron 4 of the MEN1 gene, potentially explaining the difficulties in management of this tumor. Genetic counseling and screening has now been offered to the wider family. Conclusions This case emphasizes the need to consider pituitary adenomas in the differential diagnosis of all pediatric suprasellar tumors by careful endocrine assessment and measurement of at least a serum prolactin concentration. It also highlights the lack of evidence for the optimal management of pediatric drug-resistant prolactinomas. Finally, the case we describe demonstrates the importance of a detailed family history and the role of genetic testing for MEN1 and AIP mutations in all cases of pediatric pituitary adenoma

Machine learning applied to enzyme turnover numbers reveals protein structural correlates and improves metabolic models.

Knowing the catalytic turnover numbers of enzymes is essential for understanding the growth rate, proteome composition, and physiology of organisms, but experimental data on enzyme turnover numbers is sparse and noisy. Here, we demonstrate that machine learning can successfully predict catalytic turnover numbers in Escherichia coli based on integrated data on enzyme biochemistry, protein structure, and network context. We identify a diverse set of features that are consistently predictive for both in vivo and in vitro enzyme turnover rates, revealing novel protein structural correlates of catalytic turnover. We use our predictions to parameterize two mechanistic genome-scale modelling frameworks for proteome-limited metabolism, leading to significantly higher accuracy in the prediction of quantitative proteome data than previous approaches. The presented machine learning models thus provide a valuable tool for understanding metabolism and the proteome at the genome scale, and elucidate structural, biochemical, and network properties that underlie enzyme kinetics

Spin and charge order in the vortex lattice of the cuprates: experiment and theory

I summarize recent results, obtained with E. Demler, K. Park, A. Polkovnikov, M. Vojta, and Y. Zhang, on spin and charge correlations near a magnetic quantum phase transition in the cuprates. STM experiments on slightly overdoped BSCCO (J.E. Hoffman et al., Science 295, 466 (2002)) are consistent with the nucleation of static charge order coexisting with dynamic spin correlations around vortices, and neutron scattering experiments have measured the magnetic field dependence of static spin order in the underdoped regime in LSCO (B. Lake et al., Nature 415, 299 (2002)) and LaCuO_4+y (B. Khaykovich et al., Phys. Rev. B 66, 014528 (2002)). Our predictions provide a semi-quantitative description of these observations, with only a single parameter measuring distance from the quantum critical point changing with doping level. These results suggest that a common theory of competing spin, charge and superconducting orders provides a unified description of all the cuprates.Comment: 18 pages, 7 figures; Proceedings of the Mexican Meeting on Mathematical and Experimental Physics, Mexico City, September 2001, to be published by Kluwer Academic/Plenum Press; (v2) added clarifications and updated reference

Separability problem for multipartite states of rank at most four

One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are positive semidefinite). We show that any PPT state of rank two or three is separable and has length at most four. For separable states of rank four, we show that they have length at most six. It is six only for some qubit-qutrit or multiqubit states. It turns out that any PPT entangled state of rank four is necessarily supported on a 3x3 or a 2x2x2 subsystem. We obtain a very simple criterion for the separability problem of the PPT states of rank at most four: such a state is entangled if and only if its range contains no product vectors. This criterion can be easily applied since a four-dimensional subspace in the 3x3 or 2x2x2 system contains a product vector if and only if its Pluecker coordinates satisfy a homogeneous polynomial equation (the Chow form of the corresponding Segre variety). We have computed an explicit determinantal expression for the Chow form in the former case, while such expression was already known in the latter case.Comment: 19 page

Growth in solvable subgroups of GL_r(Z/pZ)

Let $K=Z/pZ$ and let $A$ be a subset of \GL_r(K) such that is solvable. We reduce the study of the growth of $A$ under the group operation to the nilpotent setting. Specifically we prove that either $A$ grows rapidly (meaning $|A\cdot A\cdot A|\gg |A|^{1+\delta}$), or else there are groups $U_R$ and $S$, with $S/U_R$ nilpotent such that $A_k\cap S$ is large and $U_R\subseteq A_k$, where $k$ is a bounded integer and $A_k = \{x_1 x_2...b x_k : x_i \in A \cup A^{-1} \cup {1}}$. The implied constants depend only on the rank $r$ of $\GL_r(K)$. When combined with recent work by Pyber and Szab\'o, the main result of this paper implies that it is possible to draw the same conclusions without supposing that is solvable.Comment: 46 pages. This version includes revisions recommended by an anonymous referee including, in particular, the statement of a new theorem, Theorem

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

The Child Brain Computes and Utilizes Internalized Maternal Choices

As children grow, they gradually learn how to make decisions independently. However, decisions like choosing healthy but less-tasty foods can be challenging for children whose self-regulation and executive cognitive functions are still maturing. We propose a computational decision-making process in which children estimate their mother's choices for them as well as their individual food preferences. By employing functional magnetic resonance imaging during real food choices, we find that the ventromedial prefrontal cortex (vmPFC) encodes children's own preferences and the left dorsolateral prefrontal cortex (dlPFC) encodes the projected mom's choices for them at the time of children's choice. Also, the left dlPFC region shows an inhibitory functional connectivity with the vmPFC at the time of children's own choice. Our study suggests that in part, children utilize their perceived caregiver's choices when making choices for themselves, which may serve as an external regulator of decision-making, leading to optimal healthy decisions

Macroscopic nucleation phenomena in continuum media with long-range interactions

Nucleation, commonly associated with discontinuous transformations between metastable and stable phases, is crucial in fields as diverse as atmospheric science and nanoscale electronics. Traditionally, it is considered a microscopic process (at most nano-meter), implying the formation of a microscopic nucleus of the stable phase. Here we show for the first time, that considering long-range interactions mediated by elastic distortions, nucleation can be a macroscopic process, with the size of the critical nucleus proportional to the total system size. This provides a new concept of "macroscopic barrier-crossing nucleation". We demonstrate the effect in molecular dynamics simulations of a model spin-crossover system with two molecular states of different sizes, causing elastic distortions.Comment: 12 pages, 4 figures. Supplementary information accompanies this paper at http://www.nature.com/scientificreport