Single Local Maximum Research Articles

Co-evolutionary distance predictions contain flexibility information.

Co-evolution analysis can be used to accurately predict residue-residue contacts from multiple sequence alignments. The introduction of machine-learning techniques has enabled substantial improvements in precision and a shift from predicting binary contacts to predict distances between pairs of residues. These developments have significantly improved the accuracy of de novo prediction of static protein structures. With AlphaFold2 lifting the accuracy of some predicted protein models close to experimental levels, structure prediction research will move on to other challenges. One of those areas is the prediction of more than one conformation of a protein. Here, we examine the potential of residue-residue distance predictions to be informative of protein flexibility rather than simply static structure. We used DMPfold to predict distance distributions for every residue pair in a set of proteins that showed both rigid and flexible behaviour. Residue pairs that were in contact in at least one reference structure were classified as rigid, flexible or neither. The predicted distance distribution of each residue pair was analysed for local maxima of probability indicating the most likely distance or distances between a pair of residues. We found that rigid residue pairs tended to have only a single local maximum in their predicted distance distributions while flexible residue pairs more often had multiple local maxima. These results suggest that the shape of predicted distance distributions contains information on the rigidity or flexibility of a protein and its constituent residues. Supplementary data are available at Bioinformatics online.

Tetrel and Pnictogen Bonds Complement Hydrogen and Halogen Bonds in Framing the Interactional Landscape of Barbituric Acids

Experimental and theoretical studies of fluoro-, chloro-, and bromo-substituted derivatives of barbituric acid and indandione show that imide protons form short hydrogen bonds and bromine or, to a lesser extent, chlorine atoms form halogen bonds. The imide nitrogen atoms act as effective pnictogen bond donors, while C(sp2) and C(sp3) atoms act as tetrel bond donors; the resulting N···O and C···O close interactions are a distinctive feature of crystal lattices in all compounds. Importantly, halogen atoms promote the electrophilicity of C(sp3) sites and favor the formation of C(sp3)···O close contacts. Oxygen atoms of carbonyl groups of barbituric and indandione units or of water molecules function as the interaction acceptor sites: namely, they donate electron density to hydrogen, halogen, nitrogen, and carbon atoms. Modeling of various barbituric acid derivatives indicates that the positive electrostatic potentials of π-holes orthogonal to the C(sp2) carbons and σ-holes on the elongation of quasi-axial F/Cl/Br–C(sp3) bonds merge to produce a single well-defined point of the most positive electrostatic potential on one face of the barbituric acids. This single local maximum of the potential on the molecular face is close to the site occupied by the oxygen forming the C(sp3)···O, and C(sp2)···O, short contacts observed in crystals.

G 1 non-uniform Catmull-Clark surfaces

This paper develops new refinement rules for non-uniform Catmull-Clark surfaces that produce G 1 extraordinary points whose blending functions have a single local maximum. The method consists of designing an "eigen polyhedron" in R 2 for each extraordinary point, and formulating refinement rules for which refinement of the eigen polyhedron reduces to a scale and translation. These refinement rules, when applied to a non-uniform Catmull-Clark control mesh in R 3 , yield a G 1 extraordinary point.

Deformation regimes, failure and rupture of a low density polyethylene (LDPE) melt undergoing uniaxial extension

A systematic investigation of the deformation regimes, failure and physical rupture of a low density polyethylene (LDPE) sample undergoing extension at a constant rate is presented. By combining integral measurements of the tensile forces and of the tensile stresses with the in-situ visualisation of the sample within a wide range of Weissenberg numbers Wi, three distinct deformation regimes are observed. At low Wi, Wi<10, a viscous (flowing) deformation regime characterised by a single local maximum of the tensile force (engineering stress) related to the onset of a necking instability is observed. The rupture of the sample within this regime occurs via a ductile mechanism. For intermediate values of the Weissenberg number, 10⩽Wi⩽200, a transitional deformation regime characterised by a competition between the failure behaviour (primary necking) and the stabilising strain hardening (elastic) effects is observed. The physical rupture of the sample occurs via the emergence of secondary necks. As the Weissenberg number is further increased, Wi>200, the strain hardening eventually wins over the necking instability which ultimately modifies the dynamics of the physical rupture of the sample. A quasi-thermodynamic picture of the extension process at various rates of deformation and temperatures is proposed. A detailed analysis of the experimentally observed scaling properties of the relevant physical quantities measured at the failure and the rupture points is provided. The paper closes with a discussion of the main findings and their possible impact onto the current understanding of failure and rupture of polymer melts in extensional flows.

Linear stability of selfsimilar solutions of unstable thin-film equations

We study the linear stability of selfsimilar solutions of long-wave unstable thin-film equations with power-law nonlinearities u_t = −(u^n u_{xxx} + u^m u_x)_x\qquad \text{for }0 &lt; n &lt; 3, \ n≤ m. Steady states, which exist for all values of m and n above, are shown to be stable if m ≤ n + 2 when 0 &lt; n ≤ 2 , marginally stable if m ≤ n + 2 when 2 &lt; n &lt; 3 , and unstable otherwise. Dynamical selfsimilar solutions are known to exist for a range of values of n when m = n + 2 . We carry out the analysis of the stability of these solutions when n= 1 and m = 3 . Spreading selfsimilar solutions are proven to be stable. Selfsimilar blowup solutions with a single local maximum are proven to be stable, while selfsimilar blowup solutions with more than one local maximum are shown to be unstable. The equations above are gradient flows of a nonconvex energy on formal infinite-dimensional manifolds. In the special case n = 1 the equations are gradient flows with respect to the Wasserstein metric. The geometric structure of the equations plays an important role in the analysis and provides a natural way to approach a family of linear stability problems.

Yield curve shapes and the asymptotic short rate distribution in affine one-factor models

We consider a model for interest rates where the short rate is given under the risk-neutral measure by a time-homogeneous one-dimensional affine process in the sense of Duffie, Filipovic, and Schachermayer. We show that in such a model yield curves can only be normal, inverse, or humped (i.e., endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate rt. We give conditions under which the short rate process converges to a limit distribution and describe the risk-neutral limit distribution in terms of its cumulant generating function. We apply our results to the Vasicek model, the CIR model, a CIR model with added jumps, and a model of Ornstein–Uhlenbeck type.

COMPUTING THE SET OF ALL THE DISTANT HORIZONS OF A TERRAIN

We study the problem of computing the set of all distant horizons of a terrain, represented as either: (1) the set of all edges that appear on the distant horizon from at least one viewing direction; (2) for every edge e, the set of direction intervals for which e appears on the distant horizon; or (3) a search structure to query for the edges on the distant horizon, or the precise distant horizon, from a fixed viewing direction. We describe an algorithm that solves the first and second forms of the problem in O(n2+∊) time for any constant ∊ &gt; 0 where n is the number of edges of the terrain. This algorithm can be extended to compute a search structure for (3) in O(n2+∊) time. The search structure can return the s edges on the distant horizon in O( log n + s) time. We show solving problem (1) is 3SUM hard. Furthermore, we construct a terrain with a single local maximum in which Θ(n) edges each have Θ(n) direction intervals, showing that our solution to (2) cannot be significantly improved, in the worst case, even for such restricted terrains. This takes advantage of a novel construction in which the convex hull of a set of n linearly moving points, whose trajectories do not intersect, changes Ω(n2) times.

On the Eigenvalues of Zakharov--Shabat Systems

We consider the eigenvalues of a Zakharov--Shabat system on the real line with a complex-valued L1 potential and show that $\pi/2$ is the threshold L1 norm of the potential for the formation of eigenvalues. We obtain best possible lower bounds on the number of eigenvalues for a real potential of one sign. This lower bound is exact for the class of single lobe potentials, that is, positive potentials with a single local maximum that is also global.

Steady-state frictional geostrophic circulation in a one-layer ocean model with thermodynamics

Abstract The governing equations are developed for a steady-state frictional geostrophic inhomogeneous 1.5-layer ocean model, with horizontal velocity field that is linearly sheared in the vertical coordinate. We show that in the adiabatic, thermally non-diffusive limit there are an infinite number of solutions for the temperature and depth fields of the subtropical gyre even with the constraint of identical mass within each temperature range. In the non-adiabatic case, a unique subtropical gyre solution exists that can exhibit a temperature front, containing an unbounded meridional gradient, in the northwest corner of the solution domain. The role of mixing of enthalpy in the western boundary layer (WBL) region was investigated by comparing the two extreme cases of no mixing and complete mixing of enthalpy in this region. Also investigated was the dependence of the meridional heat transport on the air–sea heat exchange coefficient, κ. The temperature field was found to be strongly influenced by mixing. However, both qualitatively and quantitatively, the heat transport is similar in the model with and without mixing. The heat transport attains a single local maximum at κ=κc, that lies within values that are oceanographically relevant.

Stochastic single machine scheduling with an exponentially distributed due date

In this paper, we consider a single machine scheduling problem with random processing times to minimize the expected total weighted deviations of completion times from a random common due date. The processing times and the due date are exponentially distributed. The optimal schedules are shown to be Λ-shaped, i.e., the sequence of w iλ i (=w i/E(p i), p i is the processing time of job i) ( i=1,2,…, n) has a single local maximum, where w i and λ i denote the weight and the processing time rate of job i, respectively. Moreover, the case where the machine is subject to stochastic breakdowns is also discussed.

On the Role of Mean Curvature in Some Singularly Perturbed Neumann Problems

We construct solutions exhibiting a single spike-layer shape around some point of the boundary as $\var \to 0$ for the problem \left\{ \begin{array}{l} \var^2 \tri u - u + u^p = 0 \quad \mbox{in} \Omega, u > 0 \quad \mbox{in} \Omega, \frac{\partial u}{\partial \nu} = 0 \quad \mbox{on} \partial \Omega, \end{array} \right.\label {1.1} where $ \Omega $ is a bounded domain with smooth boundary in $R^N$, $p > 1 $, and $p< {N+2\over N-2}$ if $N\ge 3$. Our main result states that given a topologically nontrivial critical point of the mean curvature function of $\partial \Omega$, for instance, a possibly degenerate local maximum, local minimum, or saddle point, there is a solution with a single local maximum, which is located at the boundary and approaches this point as $\var\to 0$ while vanishing asymptotically elsewhere.

Photoelectric properties of lead molybdate crystals

Photoelectric properties of lead molybdate crystals including dark current-voltage characteristics and those for illuminated crystals were investigated. The current-voltage characteristics, measured for illuminated crystals, are found to have a parabolic shape with a single local maximum. A model using the Ridley-Watkins-Hilsum theory of multivalley conduction bands is proposed to explain this shape of the current-voltage characteristics. This model is also used for the interpretation of spectral dependences of both photoconductivity and absorption of the crystals. [Russian Text Ignored].

Λ-Shaped Policies to Schedule Deteriorating Jobs

We study a problem of scheduling deteriorating jobs, i.e. jobs whose processing times are an increasing function of their starting times. We consider the case of a single machine and linear job-independent deterioration. The objective is to minimize the sum of weighted completion times, with weights proportional to the basic processing times. The optimal schedule is shown to be Λ-shaped, i.e. the sequence of the basic processing times has a single local maximum. Moreover, we show that the problem is solved in O(N log N) time. In the last section we test heuristics for the case of general weights.

A nonunimodal graded gorenstein artin algebra in codimension five

A graded standard Gorenstein Artin algebra quotient of the polynomial ring R over k can be viewed as the algebra Af of partial differential operators of all degrees on a form F. The algebra A is unimodal if the Hilbert function has a single local maximum. We use the theory of compressed algebras to construct forms F in five or more variables whose Gorenstein algebras Af are not unimodal.

Component reconstruction in the primary space of spectra and concentrations. Alternating regression and related direct methods

A set of methods that extract the spectral components in a chromatographic run is considered. The methods do not need libraries of previously known spectra or retention times. The methods have been developed for two-dimensional spectra but they can also be used for chromatographic analyses with a single-channel detector. The methods are direct; they do not use principal components as the starting point. Alternating regression (AR) remains in the primary space of spectra and concentrations during the calculations. Random numbers are used as the starting spectra. Regression is used to solve first for the concentrations, then for the spectra. The method uses two kinds of constraints: all spectra and concentrations are forced to be positive; and all concentration profiles are forced to a unimodal shape with a single local maximum. It is assumed that all observations are a linear sum of components. Compact alternating regression (CAR) is a new variant of the basic AR. The idea is to replace multiplication of a large matrix by two multiplications of smaller matrices. This typically speeds up the iterations by a factor of ten. AR and CAR have been successfully used with combined techniques such as gas chromatography—mass spectrometry and liquid chromatography with UV—visible detection. The reliability of the solution is checked by repeatedly injecting noise and performing the analysis several times. This produces estimates of confidence intervals. AR and CAR have recently been extended to handle single-dimensional signals. Examples are single-channel detectors such as the flame ionization detector in gas or liquid chromatography with a fixed-wavelength UV detector. A batch of samples is used as the observation matrix. As a result, one obtains both the concentrations and the elution shapes of individual chromatographic peaks.

On the dispersion in direction of interstellar polarization

view Abstract Citations (133) References (48) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Dispersion in Direction of Interstellar Polarization Myers, P. C. ; Goodman, A. A. Abstract The spatial distribution of polarization angle is summarized for 15 dark clouds that lack prominent star formation, for four star clusters embedded in dark clouds, for one evolved cluster with little associated extinction, and for six dark cloud complexes. Most clouds have either one well-defined mean direction over their spatial extent or two or three spatial zones having noticeably different mean directions. Nearly all regions have a single local maximum in their number distribution of polarization angle. Clouds with embedded clusters have a more complex distribution of polarization direction than do clouds without clusters. It is proposed that the enhanced dispersion of polarization angle in clusters may be more closely associated with young stars and/or with dense gas, than simply with the number of stars in the cluster. The greatest dispersion in direction among clouds without clusters, 0.7 radians, occurs in L1689 in Ophiuchus. Publication: The Astrophysical Journal Pub Date: June 1991 DOI: 10.1086/170070 Bibcode: 1991ApJ...373..509M Keywords: Astronomical Photometry; Dispersion; Interstellar Magnetic Fields; Interstellar Matter; Optical Polarization; Star Clusters; Dark Matter; Line Of Sight; Magnetohydrodynamics; Probability Distribution Functions; Zeeman Effect; Astrophysics; CLUSTERS: OPEN; INTERSTELLAR: MAGNETIC FIELDS; INTERSTELLAR: MATTER; POLARIZATION full text sources ADS | data products SIMBAD (18)