Amino acid metabolism conflicts with protein diversity

The twenty protein coding amino acids are found in proteomes with different relative abundances. The most abundant amino acid, leucine, is nearly an order of magnitude more prevalent than the least abundant amino acid, cysteine. Amino acid metabolic costs differ similarly, constraining their incorporation into proteins. On the other hand, sequence diversity is necessary for protein folding, function and evolution. Here we present a simple model for a cost-diversity trade-off postulating that natural proteomes minimize amino acid metabolic flux while maximizing sequence entropy. The model explains the relative abundances of amino acids across a diverse set of proteomes. We found that the data is remarkably well explained when the cost function accounts for amino acid chemical decay. More than one hundred proteomes reach comparable solutions to the trade-off by different combinations of cost and diversity. Quantifying the interplay between proteome size and entropy shows that proteomes can get optimally large and diverse

Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.Comment: To appear in Journal of Statistical Physic

Convergence of random zeros on complex manifolds

We show that the zeros of random sequences of Gaussian systems of polynomials of increasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular, the normalized distribution of zeros of systems of m polynomials of degree N, orthonormalized on a regular compact subset K of C^m, almost surely converge to the equilibrium measure on K as the degree N goes to infinity.Comment: 16 page

The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

We consider an Euclidean supersymmetric field theory in $Z^3$ given by a supersymmetric $\Phi^4$ perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) L\'evy random walk in $Z^3$. The Green's function depends on the L\'evy-Khintchine parameter $\alpha={3+\epsilon\over 2}$ with $0<\alpha<2$. For $\alpha ={3\over 2}$ the $\Phi^{4}$ interaction is marginal. We prove for $\alpha-{3\over 2}={\epsilon\over 2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding L\'evy walk in $Z^3$ is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding L\'evy walk in $Z^3$.Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition of norms involving fermions to ensure uniqueness. 2. change in the definition of lattice blocks and lattice polymer activities. 3. Some proofs have been reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos corrected.This is the version to appear in Journal of Statistical Physic

Trivial centralizers for Axiom A diffeomorphisms

We show there is a residual set of non-Anosov $C^{\infty}$ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If $M$ is a surface and $2\leq r\leq \infty$, then we will show there exists an open and dense set of of $C^r$ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. Additionally, we examine commuting diffeomorphisms preserving a compact invariant set $\Lambda$ where $\Lambda$ is a hyperbolic chain recurrent class for one of the diffeomorphisms.Comment: 18 page

Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

Процессы турбулентных течений жидкостей в трубопроводах и каналах

The paper proposes a methodology for an analysis and calculation of processes pertaining to turbulent liquid flows in pipes and channels. Various modes of liquid motion in pipelines of thermal power devices and equipment have been considered in the paper.The presented dependences can be used while making practical calculations of losses due to friction in case of transportation of various energy carriers.Предложены методики анализа и расчета процессов турбулентного течения жидкости в трубах и каналах. Рассмотрены различные режимы движения жидкостей в трубопроводах теплоэнергетических устройств и оборудования.Представленные зависимости можно использовать при практических расчетах потерь на трение при транспортировке энергоносителей различного назначения

Should I Take Aspirin? (SITA): RCT of a decision aid for cancer chemoprevention.

Background Australian guidelines recommend that all people aged 50-70 years old consider taking low-dose aspirin to reduce the risk of colorectal cancer (CRC). Aim To determine the effect of a consultation with a researcher in general practice using a decision aid about taking low-dose aspirin to prevent CRC on informed decision-making and low-dose aspirin uptake compared to a general CRC prevention brochure. Design and Setting Individually randomised controlled trial in six general practices in Victoria, Australia, from October 2020 to March 2021. Method Patients aged 50-70 years attending a general practitioner (GP) were recruited consecutively. The intervention was a consultation using a decision aid to discuss taking aspirin to reduce CRC risk; control consultations discussed reducing CRC risk generally. The self-reported co-primary outcomes were informed choices about taking aspirin at one month and low-dose aspirin uptake at six months. Results 261 participants (86% of eligible patients) were randomised into trial arms (129 intervention, 132 control). 17.7% (20/113) of intervention and 7.6% (9/118) control participants reported making an informed choice at one month, an estimated 9.1% (95% CI 0.29% to 18.5) between-arm difference in proportions [odds ratio (OR) 2.47 (97.5% CI:0.94 to 6.52) p=0.074]. The proportions of individuals who reported using aspirin at six months were: 10.2% (12/118) intervention vs 13.8% (16/116) control (estimated between-arm difference: -4.0% (95% CI: -13.5 to 5.5); [OR= 0.68 (97.5% CI:0.27 to 1.70), p= 0.692]. Conclusion The decision aid improved informed decision-making; but has little effect on long-term regular use of aspirin to reduce CRC risk

Central Path Curvature and Iteration-Complexity for Redundant Klee—Minty Cubes

We consider a family of linear optimization problems over the n-dimensional Klee—Minty cube and show that the central path may visit all of its vertices in the same order as simplex methods do. This is achieved by carefully adding an exponential number of redundant constraints that forces the central path to take at least 2n − 2 sharp turns. This fact sug-gests that any feasible path-following interior-point method will take at least O(2n) iterations to solve this problem, whereas in practice typically only a few iterations (e.g., 50) suffices to obtain a high-quality solution. Thus, the construction potentially exhibits the worst-case iteration-complexity known to date which almost matches the theoretical iteration-complexity bound for this type of methods. In addition, this construction gives a counterexample to a conjecture that the total central path curvature is O(n)