A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method for rolling bodies on inclined planes, with applications to rescue operations.
Shapes can roll downhill following any curve, but often return to initial orientation after crossing multiple copies.
Optical interpretation of Euler's angle problem for caustics of light rays.
In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space E^{n}. Morever, we consider the pre-characterizations about inclined curves and slant helices and reconfigure them.
In this paper, we introduce an inclined curves according to parallel transport frame. Also, we define a vector field called Darboux vector field of an inclined curve in and we give a new characterization such as: "α: I \subset R \rightarrow E^4 is an inclined curve \Leftrightarrow k_1 \int k_1ds + k_2 \int \k_2 +k_3ds …
New proof confirms rolling objects can follow any path.
The paper explores invariant subbundles in nonholonomic mechanics.
We investigate contrasting behaviours emerging when studying foliations on non-metrisable manifolds. It is shown that Kneser's pathology of a manifold foliated by a single leaf cannot occur with foliations of dimension-one. On the other hand, there are open surfaces admitting no foliations. This is derived from a quali…
Study on evolving interfaces with complex curvature and density effects.
Machine learning models predict the behavior of negatively buoyant jets from wastewater.
The paper explores infinite-dimensional nonholonomic and vakonomic systems.
In this study, we have identified slant helix ( type slant helix, slant helix ( type slant helix) and attained some characteristic properties in the Euclidean 5-Space . In addition to this, we have proven that there are no other helices other than helix (inclined curve), sla…
Study on dynamic curves with elastic energy and spontaneous curvature.
Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. Its homology reproduces singular homology of M. Th…
The origin of quasiconformal mappings, like that of conformal mappings, can be traced back to old cartography where the basic problem was the search for mappings from the sphere onto the plane with minimal deviation from conformality, subject to certain conditions which were made precise. In this paper, we survey the d…
For the supervised least squares classifier, when the number of training objects is smaller than the dimensionality of the data, adding more data to the training set may first increase the error rate before decreasing it. This, possibly counterintuitive, phenomenon is known as peaking. In this work, we observe that a s…
GeoAdaLer enhances geometric understanding of Adam for stochastic optimization.
Decision tree is an important method for both induction research and data mining, which is mainly used for model classification and prediction. ID3 algorithm is the most widely used algorithm in the decision tree so far. In this paper, the shortcoming of ID3's inclining to choose attributes with many values is discusse…
Contextual policy search allows adapting robotic movement primitives to different situations. For instance, a locomotion primitive might be adapted to different terrain inclinations or desired walking speeds. Such an adaptation is often achievable by modifying a small number of hyperparameters. However, learning, when …
Optimizes information acquisition to reduce estimation risk and maximize utility.
Breiman's paper sparked debate on the future of statistics and machine learning.
We propose a statistical model for weighted temporal networks capable of measuring the level of heterogeneity in a financial system. Our model focuses on the level of diversification of financial institutions; that is, whether they are more inclined to distribute their assets equally among partners, or if they rather c…
The Chain-of-Decision approach improves forecasting of financial professionals' trading decisions.
We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are currently used to model financial markets. One of the most prominent examples is here th…
New model predicts grain boundary migration in metals.
The study finds that Chinese internet users have different search behaviors and attention patterns.
Improved model predicts wildfire spread on slopes.
This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best performance. This has led to the development of adaptive methods, that claim autom…
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to . We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plan…
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
The study classifies semiaffine stable planes into affine, projective, or punctured projective planes.
Stable planes are locally isomorphic to classical projective planes.
Only vertical planes are asymptotic to other planes in 3D space.
Study of elementary planes in Apollonian orbifold with unusual equidistribution.
Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…
Criteria for sharksfin and deltoid singularities from plane to plane, with applications.
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite met…
The study explores conformal planes with finite areas.
Human behavioural patterns exhibit selfish or competitive, as well as selfless or altruistic tendencies, both of which have demonstrable effects on human social and economic activity. In behavioural economics, such effects have traditionally been illustrated experimentally via simple games like the dictator and ultimat…
For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of th…
We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.
This thesis explores bifoliated planes and their group actions from Anosov flows.
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…
Two proofs show that removing a loop from a plane circuit splits the plane.
The paper classifies singularities of plane congruences and affine distance functions.
Computed distortion coefficients for the α-Grushin plane.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
Study compact plane waves, showing they are essentially standard.