Paper investigates reflection principles for zero mean curvature surfaces in isotropic 3-space.
problem Investigating reflection principles for zero mean curvature surfaces in isotropic 3-space.
method Analyzes reflection principles for zero mean curvature surfaces in I3. result Shows a reflection principle for isotropic line segments on zero mean curvature surfaces in I3. Modified model prevents volatility from approaching zero.
problem Volatility in the Gatheral model can approach zero, making it statistically indistinguishable.
method Proposed a modified model with Skorokhod reflection to prevent volatility from approaching zero.
result The modified model prevents volatility from approaching zero, preserving the model's flexibility.
Study proves existence of curvature-preserving metrics on balls with symmetries.
problem Existence of conformal metrics with prescribed mean curvature on balls.
method Flow method to prove existence of solutions.
result Existence of conformal metrics with prescribed mean curvature on unit balls with symmetries.
Study new BSDEs with mean reflection constraints.
problem Imposing mean reflection constraints on BSDE solutions.
method Introduced and analyzed new type of BSDEs with mean reflection constraints, proving well-posedness under natural Skorokhod condition.
result Extended results to include static risk measures, providing applications in super hedging.
The study finds billiard trajectories with infinitely many reflections in certain cones.
problem Existence of billiard trajectories with infinitely many reflections.
method Analysis of C3 convex cones and elliptic cones in R3. result Existence of C2 convex cones with billiard trajectories having infinitely many reflections. Neural network model improves leaf spectral reflectance prediction for grapevines.
problem Inaccurate modeling of grapevine leaf spectral reflectance from traits.
method Multi-head attention neural network trained on grapevine-specific data.
result Model achieved high accuracy (R^2=0.84, NRMSE=1.52%) and outperformed PROSPECT-PRO.
We consider the evolution of hypersurfaces on the unit sphere Sn+1 by their mean curvature. We prove a differential Harnack inequality for any weakly convex solution to the mean curvature flow. As an application, by applying an Aleksandrov reflection argument, we classify convex, ancient solutions of the …
An analytico-geometric reflection principle is established by means of normal deformations of analytic discs.
The study explores how to transform parallel light rays using mirror reflections.
problem Given a diffeomorphism between parallel light rays, can it be achieved by mirror reflections?
method Proves the possibility of 2-mirror realization for gradient functions and extends to higher dimensions and orientation changes.
result Gradient functions can be realized by 2 mirror reflections, and orientation reversing or preserving diffeomorphisms by 4 or 6 reflections respectively.
In this paper, we investigate the volume-prserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space. We prove that the tubeness is preserved along the flow under certain conditions.
Study on surfaces with constant anisotropic mean curvature in 3D space.
problem Characterizing surfaces with constant anisotropic mean curvature.
method Analyzing uniformly elliptic anisotropic functionals and proving properties of surfaces.
result Characterization of surfaces with constant anisotropic mean curvature.
The paper finds inequalities in Grassmannian geometry.
problem Understanding geometric properties of Grassmannians.
method Analyzes inequalities for elements in Grassmannians.
result Law of Cosines and geodesic triangle inequalities.
Study preserves tubeness of tubes in certain symmetric spaces.
problem Preserving the shape of tubes in symmetric spaces.
method Volume-preserving mean curvature flow, analyzing radius function and gradient.
result Tubeness is preserved in rank one symmetric spaces of non-compact type.
We consider spacetimes N satisfying some structural conditions, which are still fairly general, and prove convergence results for the leaves of an inverse mean curvature flow. Moreover, we define a new spacetime N^ by switching the light cone and using reflection to define a new time function, such that the two…
In this paper we investigate constant mean curvature surfaces with nonempty boundary in Euclidean space that meet a right cylinder at a constant angle along the boundary. If the surface lies inside of the cylinder, we obtain some results of symmetry by using the Alexandrov reflection method. When the mean curvature is …
Paper studies optimal tracking portfolio in mean field game of large fund competition.
problem Optimal tracking portfolio in large fund competition with relative performance benchmark.
method Formulated mean field game problem, established existence of mean field equilibrium using PDE approach, constructed approximate Nash equilibrium.
result Existence of mean field equilibrium and consistency condition verified.
In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver g is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of g-Snell enveloppe. Then, in a second step, we re…
Proposes RDASS for better Korean text summarization evaluation.
problem ROUGE scores fail to capture semantic meaning in Korean text summarization.
method Introduces RDASS metrics and a method to improve their correlation with human judgment.
result RDASS metrics correlate better with human judgment than ROUGE scores.
Develops Aleksandrov reflection for hyperbolic flows, proving convergence to umbilic surfaces.
problem Analyzing geometric flows in hyperbolic spaces.
method Aleksandrov reflection framework applied to level-set formulation, with graphical and Lipschitz estimates.
result Solutions converge exponentially fast to an umbilic hypersurface at infinity.
Optimal benchmark design varies based on costs in financial manipulation.
problem Manipulation of price benchmarks in finance.
method Analyzes empirical pattern and cost structures to determine optimal benchmark design.
result The optimal benchmark depends on the relative sizes of fixed and variable costs.
Develops algorithms to estimate trends in global temperature variability.
problem Estimating trends in cloud reflectance temperature variability.
method Two novel algorithms for dense, gridded observations over space and time.
result Evaluation of methods with simulated and real-world data.
New rigidity results for hypersurfaces in warped product manifolds and Euclidean space.
problem Rigidity of hypersurfaces in warped product manifolds and Euclidean space.
method Weighted Hsiung-Minkowski integral formulas and Brendle's inequality.
result New rigidity results for hypersurfaces in specific manifolds.
Study proves unique foliation of spacetimes by constant mean curvature surfaces.
problem Proving unique foliation of open spacetimes by constant mean curvature surfaces.
method Spatially asymptotic to Robertson-Walker spacetime, proving existence and smoothness of mean curvature function.
result Existence and smoothness of unique foliation by constant mean curvature surfaces.
Classifies ancient solutions to curvature flows on the sphere.
problem Classifying ancient solutions to curvature flows on the sphere.
method Geometric techniques including maximum principle, rigidity result, and Alexandrov reflection argument.
result Any convex, quasi-ancient solution must be stationary or a family of shrinking geodesic spheres.
KS-algebra consists of expressions constructed with four kinds operations, the minimum, maximum, difference and additively homogeneous generalized means. Five families of Z-classifiers are investigated on binary classification tasks between English phonemes. It is shown that the classifiers are able to reflect well…
We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We characterize fundamental domains of our \cmc surfaces by associated great circle polyg…
A new trading strategy using reinforcement learning for statistical arbitrage.
problem Traditional statistical arbitrage models rely on model assumptions and price deviations from a long-term mean.
method Empirical reversion time metric, reinforcement learning framework, and state space optimization.
result Optimal mean reversion strategy identified through reinforcement learning.
Study no-arbitrage conditions in 1D diffusion markets with interest rates.
problem Determining no-arbitrage conditions in 1D diffusion markets with interest rates.
method Established deterministic criteria for no-arbitrage notions in terms of scale function and speed measure.
result Revealed various effects, e.g., NIP not excluded by reflecting boundaries.
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
problem Improving numerical integration accuracy in high dimensions.
method Median-of-means sampling compared to mean-of-means using RQMC methods.
result Median-of-means sampling is superior for large sample sizes, while mean-of-means is better for smaller sample sizes.
Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
Study shows how neural networks generalize with minimal training data.
problem Understanding how neural networks generalize with limited data.
method Mean-field analysis of KL-regularized empirical risk minimization.
result Generalization error rate is O(1/n) for large n. Researchers prove existence of convex translators in slab regions in all dimensions.
problem Existence of translating solutions in slab regions.
method Proof in all dimensions n≥2; slab width πsecθ; convexity and regularity results for symmetrical translators. result Existence of convex translators in specific slab regions.
We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a diffusion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider the op…
Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring surface patches share tangent planes along common boundary curves. We call the result…
The paper explores non-minimal solitons in the sphere with unique properties.
problem Exploring soliton solutions of mean curvature flow in the unit sphere.
method Analyzing integral curves of the Hopf vector field and using symmetry properties.
result A non-minimal, complete example with topology S2n−1imesR. We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and the boundary of surface meets the boundary of the cone with a constant angle, is radially graphical if the mean curvature is non-positive with respect to the Gauss map pointing toward the domain bounded by the surf…
Study ESO valuation using mean-variance hedging in continuous time models.
problem Valuation of Employee Stock Options (ESOs) in continuous time models.
method Dynamic programming and PDE techniques.
result ESO's value expressed as expected discounted payoff with respect to an equivalent martingale measure.
Study how trading costs affect equilibrium returns in a model with heterogeneous investors.
problem How trading costs influence equilibrium returns in a model with mean-variance investors.
method Developed a continuous-time risk-sharing model with quadratic transaction costs, characterized equilibrium as solution of coupled forward-backward SDEs.
result Equilibrium returns are mean-reverting and higher for risk-averse net sellers or expanding asset supply.
A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.
The paper models SOFR and EFFR dynamics, reconciling diffusive and piecewise paths.
problem Updating interest rate models for SOFR, which is becoming a key benchmark.
method Calibrates a model to SOFR and EFFR futures prices, reconciling diffusive and piecewise paths.
result The model reflects key empirical features of SOFR dynamics and reconciles diffusive and piecewise paths.
Proposes Gaussian Processes for more accurate time-correlated measurement noise in robotics.
problem Time-correlated measurement noise in robotics applications.
method Gaussian Processes as a non-parametric model for correlated measurement noise.
result Improved performance of Kalman filtering with Gaussian Processes.
The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in Hang-Seng index is carefully investigated. It is observed that the bifurcation phenom…
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "progr…
New method produces reflections with nonseparating fixed points.
problem Constructing hyperbolic manifolds with reflective symmetries.
method Standard method for constructing closed hyperbolic manifolds.
result Fixed point sets of reflections are nonseparating.
Survey explores interactions between four conformal dynamics branches.
problem Understanding complex dynamics through different mathematical concepts.
method Examples and general results with technical tools.
result Dynamical relations between Schwarz reflection parameter spaces and anti-rational maps/ reflection groups.
One reflection suffices for orthogonal weights, reducing GPU usage.
problem Efficiently computing orthogonal weight matrices without high GPU utilization.
method Use an auxiliary neural network to compute one reflection instead of many.
result One reflection is sufficient for orthogonal weights, improving GPU utilization.
For a congruence of straight lines defined by a hypersurface in Rn+1,n≥1, and a field of reflected directions created by a point source we define the notion of intensity in a tangent direction and introduce elementary symmetric functions Sm,m=1,2,...,n, of {\it principal intensities}. The problem of exi…
This article classifies reflective hyperbolic lattices of rank 4.
problem Classifying reflective hyperbolic lattices of a specific rank.
method Using automorphism groups and reflections to classify lattices.
result Complete classification of 1.2-reflective maximal anisotropic lattices of rank 4.