Structural instability in an autophosphorylating kinase switch

We analyse a simple kinase model that exhibits bistability when there is no protein turnover, and show analytically that the property of being bistable is not necessarily conserved when degradation and synthesis of the kinase are taken into account

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations—this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor. Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al. [4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses

Ministry emphasises quality of medical training

One proposed mechanism of tumour escape from immune surveillance is tumour up-regulation of the cell surface ligan FasL, whichcan lead to apoptosis of Fas receptor (Fas) positive lymphocytes. Based upon this `coun-- rattack', we have developed a mathematical model inelAin tumour cell--lymphocyte ineA-- ction cell surface expression of Fas/FasL,an d their secreted soluble forms. The model predicts that (a) the production of soluble forms of Fas an d FasL will lead to thedown regulation of theimmun respon --fi (b) matrix metallopr otein se (MMP)ink'PTfiA ion should lead toin'x# sed membran FasLan result in a higher rate of Fas-mediated apoptosis for lymphocytesthan for tumour cells. Recen studieson can--# patient len support for theseprediction s. TheclinP-- l implication are two-fold. Firstly, the use of broad spectrum MMPin'#x tors asan`fi-- n`fi--'` cagenP may be compromised by their adverse e#ecton tumour FasL up-regulation Also, Fas/FasL insL action may havean impact on the outcome ofnA--x`#B onA in immunBB`fiAw`P-- ic trialssin` the finA common pathway of all these approaches is thetran - duction of deathsign-- swithin the tumour cell

Determinantal Point Process Attention Over Grid Codes Supports Out of Distribution Generalization

Deep neural networks have made tremendous gains in emulating human-like intelligence, and have been used increasingly as ways of understanding how the brain may solve the complex computational problems on which this relies. However, these still fall short of, and therefore fail to provide insight into how the brain supports strong forms of generalization of which humans are capable. One such case is out-of-distribution (OOD) generalization -- successful performance on test examples that lie outside the distribution of the training set. Here, we identify properties of processing in the brain that may contribute to this ability. We describe a two-part algorithm that draws on specific features of neural computation to achieve OOD generalization, and provide a proof of concept by evaluating performance on two challenging cognitive tasks. First we draw on the fact that the mammalian brain represents metric spaces using grid-like representations (e.g., in entorhinal cortex): abstract representations of relational structure, organized in recurring motifs that cover the representational space. Second, we propose an attentional mechanism that operates over these grid representations using determinantal point process (DPP-A) -- a transformation that ensures maximum sparseness in the coverage of that space. We show that a loss function that combines standard task-optimized error with DPP-A can exploit the recurring motifs in grid codes, and can be integrated with common architectures to achieve strong OOD generalization performance on analogy and arithmetic tasks. This provides both an interpretation of how grid codes in the mammalian brain may contribute to generalization performance, and at the same time a potential means for improving such capabilities in artificial neural networks.Comment: 24 pages (including Appendix), 19 figure

An Empirical Assist In Resolving The Classification Dilemma Of Workers As Either Employees Or Independent Contractors

The classification of workers as "employees" or "independent contractors" is important because the employer's legal responsibilities vary depending upon the nature of the working relationship. For federal tax purposes, the term "employee" is not clearly defined.  However, the model developed in this study is able to correctly classify 96.6 percent of the judicial decisions (1980-2005) involving the status of a worker as either an employee or independent contractor.  Also, the model demonstrates stability over time and between judicial venues

An Empirical Assist In Resolving The Classification Dilemma Of Workers As Either Employees Or Independent Contractors

The classification of workers as "employees" or "independent contractors" is important because the employer's legal responsibilities vary depending upon the nature of the working relationship. For federal tax purposes, the term "employee" is not clearly defined.  However, the model developed in this study is able to correctly classify 96.6 percent of the judicial decisions (1980-2005) involving the status of a worker as either an employee or independent contractor.  Also, the model demonstrates stability over time and between judicial venues

Mathematical modelling of fluid flow and solute transport to define operating parameters for in vitro perfusion cell culture systems

In recent years, there has been a move away from the use of static in vitro two-dimensional cell culture models for testing the chemical safety and efficacy of drugs. Such models are increasingly being replaced by more physiologically relevant cell culture systems featuring dynamic flow and/or three-dimensional structures of cells. While it is acknowledged that such systems provide a more realistic environment within which to test drugs, progress is being hindered by a lack of understanding of the physical and chemical environment that the cells are exposed to. Mathematical and computational modelling may be exploited in this regard to unravel the dependency of the cell response on spatio-temporal differences in chemical and mechanical cues, thereby assisting with the understanding and design of these systems. In this paper, we present a mathematical modelling framework that characterizes the fluid flow and solute transport in perfusion bioreactors featuring an inlet and an outlet. To demonstrate the utility of our model, we simulated the fluid dynamics and solute concentration profiles for a variety of different flow rates, inlet solute concentrations and cell types within a specific commercial bioreactor chamber. Our subsequent analysis has elucidated the basic relationship between inlet flow rate and cell surface flow speed, shear stress and solute concentrations, allowing us to derive simple but useful relationships that enable prediction of the behaviour of the system under a variety of experimental conditions, prior to experimentation. We describe how the model may used by experimentalists to define operating parameters for their particular perfusion cell culture systems and highlight some operating conditions that should be avoided. Finally, we critically comment on the limitations of mathematical and computational modelling in this field, and the challenges associated with the adoption of such methods

Learning Representations that Support Extrapolation

Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to interpolation between data points in their training corpora. In this paper, we consider the challenge of learning representations that support extrapolation. We introduce a novel visual analogy benchmark that allows the graded evaluation of extrapolation as a function of distance from the convex domain defined by the training data. We also introduce a simple technique, temporal context normalization, that encourages representations that emphasize the relations between objects. We find that this technique enables a significant improvement in the ability to extrapolate, considerably outperforming a number of competitive techniques.Comment: ICML 202

Identification of methylated proteins in the yeast small ribosomal subunit: A role for SPOUT methyltransferases in protein arginine methylation

We have characterized the posttranslational methylation of Rps2, Rps3, and Rps27a, three small ribosomal subunit proteins in the yeast Saccharomyces cerevisiae, using mass spectrometry and amino acid analysis. We found that Rps2 is substoichiometrically modified at arginine-10 by the Rmt1 methyltransferase. We demonstrated that Rps3 is stoichiometrically modified by ω- monomethylation at arginine-146 by mass spectrometric and site-directed mutagenic analyses. Substitution of alanine for arginine at position 146 is associated with slow cell growth, suggesting that the amino acid identity at this site may influence ribosomal function and/or biogenesis. Analysis of the three-dimensional structure of Rps3 in S. cerevisiae shows that arginine-146 makes contacts with the small subunit rRNA. Screening of deletion mutants encoding potential yeast methyltransferases revealed that the loss of the YOR021C gene results in the absence of methylation of Rps3. We demonstrated that recombinant Yor021c catalyzes ω-monomethylarginine formation when incubated with S-adenosylmethionine and hypomethylated ribosomes prepared from a YOR021C deletion strain. Interestingly, Yor021c belongs to the family of SPOUT methyltransferases that, to date, have only been shown to modify RNA substrates. Our findings suggest a wider role for SPOUT methyltransferases in nature. Finally, we have demonstrated the presence of a stoichiometrically methylated cysteine residue at position 39 of Rps27a in a zinc-cysteine cluster. The discovery of these three novel sites of protein modification within the small ribosomal subunit will now allow for an analysis of their functional roles in translation and possibly other cellular processes. © 2012 American Chemical Society

The Relational Bottleneck as an Inductive Bias for Efficient Abstraction

A central challenge for cognitive science is to explain how abstract concepts are acquired from limited experience. This effort has often been framed in terms of a dichotomy between empiricist and nativist approaches, most recently embodied by debates concerning deep neural networks and symbolic cognitive models. Here, we highlight a recently emerging line of work that suggests a novel reconciliation of these approaches, by exploiting an inductive bias that we term the relational bottleneck. We review a family of models that employ this approach to induce abstractions in a data-efficient manner, emphasizing their potential as candidate models for the acquisition of abstract concepts in the human mind and brain