The curse of dimensionality in operator learning

Neural operator architectures employ neural networks to approximate operators mapping between Banach spaces of functions; they may be used to accelerate model evaluations via emulation, or to discover models from data. Consequently, the methodology has received increasing attention over recent years, giving rise to the rapidly growing field of operator learning. The first contribution of this paper is to prove that for general classes of operators which are characterized only by their $C^r$- or Lipschitz-regularity, operator learning suffers from a curse of dimensionality, defined precisely here in terms of representations of the infinite-dimensional input and output function spaces. The result is applicable to a wide variety of existing neural operators, including PCA-Net, DeepONet and the FNO. The second contribution of the paper is to prove that the general curse of dimensionality can be overcome for solution operators defined by the Hamilton-Jacobi equation; this is achieved by leveraging additional structure in the underlying solution operator, going beyond regularity. To this end, a novel neural operator architecture is introduced, termed HJ-Net, which explicitly takes into account characteristic information of the underlying Hamiltonian system. Error and complexity estimates are derived for HJ-Net which show that this architecture can provably beat the curse of dimensionality related to the infinite-dimensional input and output function spaces

The Nonlocal Neural Operator: Universal Approximation

Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engineering, due to their potential both to accelerate traditional numerical methods and to enable data-driven discovery. A popular variant of neural operators is the Fourier neural operator (FNO). Previous analysis proving universal operator approximation theorems for FNOs resorts to use of an unbounded number of Fourier modes and limits the basic form of the method to problems with periodic geometry. Prior work relies on intuition from traditional numerical methods, and interprets the FNO as a nonstandard and highly nonlinear spectral method. The present work challenges this point of view in two ways: (i) the work introduces a new broad class of operator approximators, termed nonlocal neural operators (NNOs), which allow for operator approximation between functions defined on arbitrary geometries, and includes the FNO as a special case; and (ii) analysis of the NNOs shows that, provided this architecture includes computation of a spatial average (corresponding to retaining only a single Fourier mode in the special case of the FNO) it benefits from universal approximation. It is demonstrated that this theoretical result unifies the analysis of a wide range of neural operator architectures. Furthermore, it sheds new light on the role of nonlocality, and its interaction with nonlinearity, thereby paving the way for a more systematic exploration of nonlocality, both through the development of new operator learning architectures and the analysis of existing and new architectures

Direct and Absolute Quantification of over 1800 Yeast Proteins via Selected Reaction Monitoring

Defining intracellular protein concentration is critical in molecular systems biology. Although strategies for determining relative protein changes are available, defining robust absolute values in copies per cell has proven significantly more challenging. Here we present a reference data set quantifying over 1800 Saccharomyces cerevisiae proteins by direct means using protein-specific stable-isotope labeled internal standards and selected reaction monitoring (SRM) mass spectrometry, far exceeding any previous study. This was achieved by careful design of over 100 QconCAT recombinant proteins as standards, defining 1167 proteins in terms of copies per cell and upper limits on a further 668, with robust CVs routinely less than 20%. The selected reaction monitoring-derived proteome is compared with existing quantitative data sets, highlighting the disparities between methodologies. Coupled with a quantification of the transcriptome by RNA-seq taken from the same cells, these data support revised estimates of several fundamental molecular parameters: a total protein count of ∼100 million molecules-per-cell, a median of ∼1000 proteins-per-transcript, and a linear model of protein translation explaining 70% of the variance in translation rate. This work contributes a “gold-standard” reference yeast proteome (including 532 values based on high quality, dual peptide quantification) that can be widely used in systems models and for other comparative studies. Reliable and accurate quantification of the proteins present in a cell or tissue remains a major challenge for post-genome scientists. Proteins are the primary functional molecules in biological systems and knowledge of their abundance and dynamics is an important prerequisite to a complete understanding of natural physiological processes, or dysfunction in disease. Accordingly, much effort has been spent in the development of reliable, accurate and sensitive techniques to quantify the cellular proteome, the complement of proteins expressed at a given time under defined conditions (1). Moreover, the ability to model a biological system and thus characterize it in kinetic terms, requires that protein concentrations be defined in absolute numbers (2, 3). Given the high demand for accurate quantitative proteome data sets, there has been a continual drive to develop methodology to accomplish this, typically using mass spectrometry (MS) as the analytical platform. Many recent studies have highlighted the capabilities of MS to provide good coverage of the proteome at high sensitivity often using yeast as a demonstrator system (4⇓⇓⇓⇓⇓–10), suggesting that quantitative proteomics has now “come of age” (1). However, given that MS is not inherently quantitative, most of the approaches produce relative quantitation and do not typically measure the absolute concentrations of individual molecular species by direct means. For the yeast proteome, epitope tagging studies using green fluorescent protein or tandem affinity purification tags provides an alternative to MS. Here, collections of modified strains are generated that incorporate a detectable, and therefore quantifiable, tag that supports immunoblotting or fluorescence techniques (11, 12). However, such strategies for copies per cell (cpc) quantification rely on genetic manipulation of the host organism and hence do not quantify endogenous, unmodified protein. Similarly, the tagging can alter protein levels - in some instances hindering protein expression completely (11). Even so, epitope tagging methods have been of value to the community, yielding high coverage quantitative data sets for the majority of the yeast proteome (11, 12). MS-based methods do not rely on such nonendogenous labels, and can reach genome-wide levels of coverage. Accurate estimation of absolute concentrations i.e. protein copy number per cell, also usually necessitates the use of (one or more) external or internal standards from which to derive absolute abundance (4). Examples include a comprehensive quantification of the Leptospira interrogans proteome that used a 19 protein subset quantified using selected reaction monitoring (SRM)1 to calibrate their label-free data (8, 13). It is worth noting that epitope tagging methods, although also absolute, rely on a very limited set of standards for the quantitative western blots and necessitate incorporation of a suitable immunogenic tag (11). Other recent, innovative approaches exploiting total ion signal and internal scaling to estimate protein cellular abundance (10, 14), avoid the use of internal standards, though they do rely on targeted proteomic data to validate their approach. The use of targeted SRM strategies to derive proteomic calibration standards highlights its advantages in comparison to label-free in terms of accuracy, precision, dynamic range and limit of detection and has gained currency for its reliability and sensitivity (3, 15⇓–17). Indeed, SRM is often referred to as the “gold standard proteomic quantification method,” being particularly well-suited when the proteins to be quantified are known, when appropriate surrogate peptides for protein quantification can be selected a priori, and matched with stable isotope-labeled (SIL) standards (18⇓–20). In combination with SIL peptide standards that can be generated through a variety of means (3, 15), SRM can be used to quantify low copy number proteins, reaching down to ∼50 cpc in yeast (5). However, although SRM methodology has been used extensively for S. cerevisiae protein quantification by us and others (19, 21, 22), it has not been used for large protein cohorts because of the requirement to generate the large numbers of attendant SIL peptide standards; the largest published data set is only for a few tens of proteins. It remains a challenge therefore to robustly quantify an entire eukaryotic proteome in absolute terms by direct means using targeted MS and this is the focus of our present study, the Census Of the Proteome of Yeast (CoPY). We present here direct and absolute quantification of nearly 2000 endogenous proteins from S. cerevisiae grown in steady state in a chemostat culture, using the SRM-based QconCAT approach. Although arguably not quantification of the entire proteome, this represents an accurate and rigorous collection of direct yeast protein quantifications, providing a gold-standard data set of endogenous protein levels for future reference and comparative studies. The highly reproducible SIL-SRM MS data, with robust CVs typically less than 20%, is compared with other extant data sets that were obtained via alternative analytical strategies. We also report a matched high quality transcriptome from the same cells using RNA-seq, which supports additional calculations including a refined estimate of the total protein content in yeast cells, and a simple linear model of translation explaining 70% of the variance between RNA and protein levels in yeast chemostat cultures. These analyses confirm the validity of our data and approach, which we believe represents a state-of-the-art absolute quantification compendium of a significant proportion of a model eukaryotic proteome

Safety and effectiveness of bariatric surgery: Roux-en-Y gastric bypass is superior to gastric banding in the management of morbidly obese patients

<p>Abstract</p> <p>Background</p> <p>The use of bariatric surgery in the management of morbid obesity is rapidly increasing. The two most frequently performed procedures are laparoscopic Roux-en-Y bypass and laparoscopic gastric banding. The objective of this short overview is to provide a critical appraisal of the most relevant scientific evidence comparing laparoscopic gastric banding versus laparoscopic Roux-en-Y bypass in the treatment of morbidly obese patients.</p> <p>Results and discussion</p> <p>There is mounting and convincing evidence that laparoscopic gastric banding is suboptimal at best in the management of morbid obesity. Although short-term morbidity is low and hospital length of stay is short, the rates of long-term complications and band removals are high, and failure to lose weight after laparoscopic gastric banding is prevalent.</p> <p>Conclusion</p> <p>The placement of a gastric band appears to be a disservice to many morbidly obese patients and therefore, in the current culture of evidence based medicine, the prevalent use of laparoscopic gastric banding can no longer be justified. Based on the current scientific literature, the laparoscopic gastric bypass should be considered the treatment of choice in the management of morbidly obese patients.</p

Modelling of advanced three-ion ICRF heating and fast ion generation scheme for tokamaks and stellarators

Absorption of ion-cyclotron range of frequencies waves at the fundamental resonance is an efficient source of plasma heating and fast ion generation in tokamaks and stellarators. This heating method is planned to be exploited as a fast ion source in the Wendelstein 7-X stellarator. The work presented here assesses the possibility of using the newly developed three-ion species scheme (Kazakov et al (2015) Nucl. Fusion 55 032001) in tokamak and stellarator plasmas, which could offer the capability of generating more energetic ions than the traditional minority heating scheme with moderate input power. Using the SCENIC code, it is found that fast ions in the MeV range of energy can be produced in JET-like plasmas. The RF-induced particle pinch is seen to strongly impact the fast ion pressure profile in particular. Our results show that in typical high-density W7-X plasmas, the three-ion species scheme generates more energetic ions than the more traditional minority heating scheme, which makes three-ion scenario promising for fast-ion confinement studies in W7-X

Novel, synergistic antifungal combinations that target translation fidelity

There is an unmet need for new antifungal or fungicide treatments, as resistance to existing treatments grows. Combination treatments help to combat resistance. Here we develop a novel, effective target for combination antifungal therapy. Different aminoglycoside antibiotics combined with different sulphate-transport inhibitors produced strong, synergistic growth-inhibition of several fungi. Combinations decreased the respective MICs by ≥8 fold. Synergy was suppressed in yeast mutants resistant to effects of sulphate-mimetics (like chromate or molybdate) on sulphate transport. By different mechanisms, aminoglycosides and inhibition of sulphate transport cause errors in mRNA translation. The mistranslation rate was stimulated up to 10-fold when the agents were used in combination, consistent with this being the mode of synergistic action. A range of undesirable fungi were susceptible to synergistic inhibition by the combinations, including the human pathogens Candida albicans, C. glabrata and Cryptococcus neoformans, the food spoilage organism Zygosaccharomyces bailii and the phytopathogens Rhizoctonia solani and Zymoseptoria tritici. There was some specificity as certain fungi were unaffected. There was no synergy against bacterial or mammalian cells. The results indicate that translation fidelity is a promising new target for combinatorial treatment of undesirable fungi, the combinations requiring substantially decreased doses of active components compared to each agent alone

The Evolution of Expressing and Exchanging Cyber-Investigation Information in a Standardized Form

The growing number of investigations involving digital traces from various data sources is driving the demand for a standard way to represent and exchange pertinent information. Enabling automated combination and correlation of cyber-investigation information from multiple systems or organizations enables more efficient and comprehensive analysis, reducing the risk of mistakes and missed opportunities. These needs are being met by the evolving open-source, community-developed specification language called CASE, the Cyber-investigation Analysis Standard Expression. CASE leverages the Unified Cyber Ontology (UCO), which abstracts and expresses concepts that are common across multiple domains. This paper introduces CASE and UCO, explaining how they improve upon prior related work. The value of fully-structured data, representing provenance, and action lifecycles are discussed. The guiding principles of CASE and UCO are presented, and illustrative examples of CASE are provided using the default JSON-LD serialization