Machine learning corrects ion interference in nutrient solutions.
problem Ion imbalance and excessive salt accumulation in hydroponic systems.
method Machine learning approach to correct ion sensor data affected by ion interference.
result Readjusted ion sensor data showed high accuracy (91.6-98.3%).
Machine learning models estimate nutrient concentrations from water quality surrogates.
problem Estimating high frequency nutrient concentrations from limited in-situ measurements.
method Used machine learning (Random Forests) to estimate nutrient concentrations using surrogate measures.
result Reduced RMSE by up to 60.1% compared to linear models, with additional sensors not providing significant benefits.
New method estimates effects of multiple nutrients on blood glucose.
problem Estimating physiological response to multiple nutrient treatments.
method Convolution-based multi-output Gaussian process model.
result Improved prediction accuracy and better interpretation of individual nutrient effects.
Develops adaptive algorithms for sustainable fertilizer use in agriculture.
problem Sustaining high yields while reducing environmental impacts of fertilizer use.
method Nonlinear model-based bandit algorithms linking biological processes to decision-making.
result Faster learning and higher profits with interpretable recommendations.
Celiac Disease (CD) and Environmental Enteropathy (EE) are common causes of malnutrition and adversely impact normal childhood development. CD is an autoimmune disorder that is prevalent worldwide and is caused by an increased sensitivity to gluten. Gluten exposure destructs the small intestinal epithelial barrier, res…
Model predicts phytoplankton subpopulations based on environmental factors.
problem Predicting phytoplankton dynamics under changing environmental conditions.
method Sparse mixture of multivariate regressions model.
result Identifies environmental covariates influencing phytoplankton subpopulations.
Work maximization guides machine learning models in adaptive systems.
problem How machine learning models can be optimized for thermodynamic efficiency.
method Introducing thermodynamic principle to compare with maximum-likelihood principle.
result Maximum-work models are equivalent to maximum-likelihood models in adaptive systems.
Method selects significant spatial covariates in noisy data.
problem Identifying true spatial covariates in noisy data.
method Combines sparsity-promoting estimation with noise-robust model selection.
result Method reliably recovers true covariates under diverse noise scenarios.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
problem Inferring protein production kinetics in dividing cells due to protein inheritance and division history.
method Adapted conditional normalizing flows to approximate intractable likelihoods from simulated data.
result Glc3 gene is mostly inactive under stress, with brief and transient expression.
New method clusters hydrological and sediment data for storm event analysis.
problem Analyzing storm events for water quality constituents like turbidity.
method Multivariate time series clustering of river discharge and sediment data.
result Clusters differ from 2-D hysteresis loop classifications.
The paper examines partial regularity of Lipschitz solutions to minimal surface system.
problem Understanding the regularity of solutions to the minimal surface system.
method Investigation of stationary, integral weak, and viscosity solutions; interior gradient estimate using maximum principle.
result Partial regularity results for Lipschitz solutions, including interior gradient estimate.
Unique ancient solutions found for anisotropic curve shortening flow.
problem Finding unique solutions for anisotropic curve shortening flow.
method Constructing translating and ancient solutions under given conditions.
result Unique ancient and translating solutions found for anisotropic curve shortening flow.
The paper constructs solutions to a critical Dirac equation on spheres.
problem Solving the critical Dirac equation on spheres with singularities.
method Constructing Delaunay-type solutions and another kind of singular solutions.
result The constructed solutions are building blocks for singular solutions on Spin manifolds.
Paper classifies ancient solutions to 3D Ricci flow.
problem Classifying ancient solutions to 3D Ricci flow.
method Proves uniqueness of solutions based on classification criteria.
result Ancient solutions are either shrinking spheres or Perelman's Type II solutions.
New findings on κ-solutions with round cylinder as asymptotic shrinker.
problem Characterizing κ-solutions with specific asymptotic behavior. method Analysis of Ricci flow in dimensions n≥4. result Uniformly Positive Isoperimetric Constant (PIC) for κ-solutions. Study higher-dimensional Ricci flow solutions, proving uniqueness.
problem Classifying ancient solutions to the Ricci flow on Sn. method Extending [13] to higher dimensions, proving uniqueness.
result Ancient solutions are either shrinking spheres or Type II solutions.
Ancient solutions of Ricci flow with Type I growth are classified.
problem Understanding ancient solutions of Ricci flow with specific curvature growth.
method Analyzing ancient solutions with Type I curvature growth in arbitrary dimensions.
result Ancient solutions with Type I growth are classified into specific types.
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with s>23. The theory of maximal asymptotically Euclidean solutions of the constraint equations descends completely the low regularity setting. Moreove…
Researchers find entire solutions to magnetic Ginzburg-Landau equations in 4D.
problem Finding entire solutions to magnetic Ginzburg-Landau equations in 4D.
method Using Lyapunov-Schmidt reduction.
result Existence of entire solutions and saddle type solutions with specific zero sets.
New ancient solutions found for curvature flow in 2D.
problem Ancient solutions for curvature flow in 2D.
method Constructing and classifying convex ancient solutions.
result All convex ancient solutions classified for α∈(32,1). Let n≥3 and m=n+2n−2. We construct 5-parameters, 4-parameters, 3-parameters ancient solutions of the equation vt=(vm)xx+v−vm, v>0, in R×(−∞,T) for some T∈R. This equation arises in the study of Yamabe flow. We obtain various properties of the ancient so…
We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.
Minimax solutions are weak solutions to Cauchy problems involving Hamilton--Jacobi equations, constructed from generating families quadratic at infinity of their geometric solutions. We give a complete description of minimax solutions and we classify their generic singularities of codimension not greater than 2.
Paper shows how solutions to Allen-Cahn converge to multiphase mean curvature flow.
problem Convergence of Allen-Cahn solutions to multiphase mean curvature flow.
method Conditional convergence result of Allen-Cahn solutions to De Giorgi type BV-solutions of multiphase mean curvature flow.
result De Giorgi type BV-solutions are unique in a weak-strong sense.
We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.
The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.
Generic level sets in mean curvature flow are BV solutions.
problem Understanding the behavior of level sets in mean curvature flow.
method Using the framework of sets of finite perimeter and distributional solutions, the paper extends Evans and Spruck's work.
result Generic level sets are distributional solutions with optimal energy dissipation rate.
Real analytic solutions found for special Lagrangian equation.
problem Analyzing convex solutions of the special Lagrangian equation.
method Interior regularity established for convex viscosity solutions.
result All convex solutions are real analytic in the interior.
Proves existence and uniqueness of viscosity solutions to complex Hessian equations on compact Hermitian manifolds.
problem Existence and uniqueness of viscosity solutions to complex Hessian equations.
method Proves existence and uniqueness using viscosity solutions and determinant domination conditions.
result Viscosity solutions exist and are unique under certain conditions.
In this paper we study the difference between algebraic and geometric solutions of the hyperbolic Dehn filling equations for ideally triangulated 3-manifolds. We show that any geometric solution is an algebraic one, and we prove the uniqueness of the geometric solutions. Then we do explicit calculations for three inter…
Study finds solutions to Yamabe equation with specific behavior near singular points.
problem Existence of solutions with prescribed asymptotic behavior near singular points of the Yamabe equation.
method Analysis of positive solutions with isolated singularities and asymptotic expansions.
result Existence of solutions with arbitrarily high order of approximation near singular points.
Study shows various weak solutions to complex flows match, proving viscosity equals pluripotential.
problem Comparing weak solutions to complex Monge-Ampère flows.
method Examined various notions of weak subsolutions and showed they coincide.
result Viscosity solution equals pluripotential solution.
Novikov equation symmetries, solutions, and pseudo-spherical surfaces studied.
problem Analyzing geometrically integrable Novikov equation properties.
method Lie symmetries, group-invariant solutions, conservation laws, unique continuation, pseudo-spherical surfaces.
result Classification of invariant solutions and existence of analytic metrics for pseudo-spherical surfaces.
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. Th…
Ancient solutions to mean curvature flow have unique shapes.
problem Understanding unique shapes of ancient solutions.
method Proved a Bernstein theorem for ancient solutions.
result Ancient solutions to mean curvature flow have unique shapes.
Ozawa solution describes surface deformation from Davey-Stewartson II equation.
problem Surface deformation ruled by the Ozawa solution of Davey-Stewartson II equation.
method Soliton deformation of surfaces ruled by the Ozawa solution.
result Explicit singularity of deformed surface at blow-up moment of Ozawa solution.
Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many noncompact, but complete solutions can be obtained in this manner, including the multi-membrane solution initially found by Duff and Stelle. In a diff…
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study, instead of the single optimal solution, we consider finding a set of diverse yet nea…
Study ancient Ricci flow solutions, proving unique asymptotic behavior.
problem Understanding unique asymptotics of compact ancient solutions to 3D Ricci flow.
method Analyzing noncollapsed compact ancient solutions, proving asymptotic behavior.
result Proves unique asymptotic behavior for compact ancient solutions.
Paper finds singular solutions for a specific physics problem on a sphere.
problem Existence of singular solutions to the conformal Dirac-Einstein system.
method Constructs a family of singular solutions on the 3D sphere.
result Constructs solutions with exactly two singularities.
Ancient pancakes solve mean curvature flow problem.
problem Mean curvature flow problem
method Constructing an embedded ancient solution as a stack of pancakes
result Embedded ancient solution to mean curvature flow
Type II (ancient) solutions to the Ricci flow on surfaces are not yet classified. It is conjectured that the Rosenau solution and the cigar are the only solutions, modulo scaling. In this paper, we mainly study the backward limit and the circumference at spatial infinity of Type II ancient solutions on noncompact surfa…
Study properties of solutions with singularities in the negative cone.
problem Properties of solutions with singularities in the negative cone.
method Proved PDE for trace and normal derivatives, showed hypersurface is minimal for k=2.
result Hypersurface is minimal for k=2 and satisfies certain PDE.
Ancient solutions to Ricci flow in higher dimensions are mostly cylinders or solitons.
problem Uniqueness of ancient κ-solutions in higher dimensions. method Analysis of ancient κ-solutions with specific properties. result The only noncompact ancient κ-solutions are cylinders, quotients, or the Bryant soliton. We study solutions of the mean curvature flow which are defined for all negative curvature times, usually called ancient solutions. We give various conditions ensuring that a closed convex ancient solution is a shrinking sphere. Examples of such conditions are: a uniform pinching condition on the curvatures, a suitable…
We consider solutions of Kapustin-Witten equation with Nahm pole boundary on S3×R+. These solutions are usually called Nahm pole solutions. In this paper, we will prove that there exists a constant C>0 such that ∥FA∥L2≤C for any Nahm pole solution (A,φ).
Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.
problem Characterizing ancient solutions on an infinite strip with polynomial and exponential growth.
method Analyzing parabolic equations on an infinite strip, proving properties of ancient solutions.
result Ancient solutions on the strip are constant if they grow polynomially, and have a finite-dimensional space for slower exponential growth.
We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of P.Daskalopoulos, R.Hamilton and N.Sesum on the a priori estimates for the ancient solutions of Ricci flow on surfaces. We also give a simple proof for the solut…