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.
Plane Delaunay triangulations are rigid under Luo's discrete conformal change.
Bitcoin volatility analysis shows decreasing HE with longer sampling periods.
Cryptotree enables accurate predictions on encrypted data using Random Forests.
The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this s…
Advances AT with HE to improve model robustness.
Mini-Hes improves LFA model performance on HDI tasks with missing data.
A Bayesian agent learns about the structure of a stationary process from ob- serving past outcomes. We prove that his predictions about the near future become ap- proximately those he would have made if he knew the long run empirical frequencies of the process.
A hybrid model combines BPH and HE distributions for better heavy-tailed distribution approximation.
Study solves sub-Laplacian equivalence on a specific Heisenberg group.
We review some ideas of Grothendieck and others on actions of the absolute Galois group Γ Q of Q (the automorphism group of the tower of finite extensions of Q), related to the geometry and topology of surfaces (mapping class groups, Teichm{ü}ller spaces and moduli spaces of Riemann surfaces). Grothendieck's motivation…
Paper finds how Steklov eigenvalues change on graphs and trees.
In this paper we consider a modification of the classical Merton portfolio optimization problem. Namely, an investor can trade in financial asset and consume his capital. He is additionally endowed with a one unit of an indivisible asset which he can sell at any time. We give a numerical example of calculating the opti…
The paper discusses Nirenberg's work on geometric problems and his personality.
Georg de Buquoy, Lord de Vaux, lived in Nove Hrady, Prague and Cerveny Hradek for most of his productive life. From his extensive scientific contributions, both theoretical and experimental, we expand here the discussion of his contributions to mathematical economy. He is mainly celebrated as the first persons to defin…
The paper proves rigidity and uniformization theorems for infinite circle patterns and convex polyhedra in hyperbolic 3-space.
T. Mochizuki constructs a theory of variations of wild Hodge structure for which the underlying flat connection can have irregular singularities at infinity. He extends in this way the correspondence of Corlette and Simpson between irreducible flat bundles and stables Higgs bundles, taking into account objects with irr…
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
In 2003, S.-s. Chern began a study of almost-complex structures on the 6-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group . While he did not solve the (currently still open) problem of determining whether there exists an int…
Grötzsch's papers review progress in quasiconformal geometry.
In his 1954 paper about the initial value problem for 2D hyperbolic nonlinear PDEs, P. Lax declared that he had "a strong reason to believe" that there must exist a well-defined class of "not genuinely nonlinear" nonlinear PDEs. In 1978 G. Boillat coined the term "completely exceptional" to denote it. In the case of $2…
Ejiri gave a negative answer to a conjecture of Lichnerowicz concerning Riemannian manifolds with constant scalar curvature admitting an infinitesimal non isometric conformal transformation. With this aim he constructed a warped product of a circle of lenght and a compact manifold. But he omitted in his analysis th…
Characterizes infinite ideal polyhedra in hyperbolic 3-space and proves their existence and rigidity.
Study the geometry and symmetries of moduli spaces of connections on KT manifolds.
A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion fluctuations. The consumption rate is subject to an upper bound constraint which linea…
Developing a singular dimension descent method for positive scalar curvature obstructions
In [Duke Math. J. 101 (1999) 359-426], Mikhail Khovanov constructed a homology theory for oriented links, whose graded Euler characteristic is the Jones polynomial. He also explained how every link cobordism between two links induces a homomorphism between their homology groups, and he conjectured the invariance (up to…
Improved optimal regularity for harmonic almost complex structures.
We outline a framework which generalizes Felix Klein's Erlanger Programm which he announced in 1872 after exchanging ideas with Sophus Lie.
Solves Brezis' first open problem on ball solutions.
We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on coming from a construction of the Geometric Invariant Theory (G.I.T). These metrics are balanced in the sense of S.K. Donaldson.…
Proves positive mass theorem for hyperbolic manifolds with ends.
This paper describes the work of Jesse Douglas on the Plateau problem, work for which he was awarded a Fields Medal in 1936, and considers the contributions Tibor Rado made in the 1930s.
Two classes of gamma-ray bursts (GRBs), short and long, have been determined without any doubts, and are usually ascribed to different progenitors, yet these classes overlap for a variety of descriptive parameters. A subsample of 46 long and 22 short GRBs with estimated Hurst Exponents (HEs), complemented by mi…
Tissot's indicatrix theory is foundational for quasiconformal mappings.
The paper proves existence of solutions to Kazdan-Warner equations on finite graphs.
Corrects a mistake in -block cross-validation consistency claim.
We give a twistorial interpretation of geometric structures on a Riemannian manifold, as sections of homogeneous fibre bundles, following an original insight by Wood (2003). The natural Dirichlet energy induces an abstract harmonicity condition, which gives rise to a geometric gradient flow. We establish a number of an…
For a 3-manifold M, McMullen derived from the Alexander polynomial of M a norm on H^1(M, R) called the Alexander norm. He showed that the Thurston norm on H^1(M, R), which measures the complexity of a dual surface, is an upper bound for the Alexander norm. He asked if these two norms were equal on all of H^1(M,R) when …
This paper formalizes manifolds in positive characteristic varieties.
We prove a conjecture of Rozansky's concerning his categorification of the tail of the colored Jones polynomial for an -adequate link. We show that the tail homology groups he constructs are trivial for non -adequate links.
Donoho's JCGS (in press) paper is a spirited call to action for statisticians, who he points out are losing ground in the field of data science by refusing to accept that data science is its own domain. (Or, at least, a domain that is becoming distinctly defined.) He calls on writings by John Tukey, Bill Cleveland, and…
The moduli space of Hermitian-Einstein connections on certain manifolds has a strong Kähler with torsion structure.
We consider an adversarial online learning setting where a decision maker can choose an action in every stage of the game. In addition to observing the reward of the chosen action, the decision maker gets side observations on the reward he would have obtained had he chosen some of the other actions. The observation str…
We prove a estimate for solutions of a class of fully nonlinear equations introduced by Chen-He. As an application, we prove the regularity of geodesics in the space of volume forms.
In the last decade, deep learning algorithms have become very popular thanks to the achieved performance in many machine learning and computer vision tasks. However, most of the deep learning architectures are vulnerable to so called adversarial examples. This questions the security of deep neural networks (DNN) for ma…
Consider an agent who enters a financial market on day t = 0 with an initial capital amount x. He invests this amount on stocks and the money market, and by day t = T, has generated a wealth W . He is given a convex class of probability measures (called scenarios) and a real-valued function (or floors) corresponding to…
In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a possible candidate for such an operator but unfortunately it proves out to be badly di…
Freedman, He, and Wang, conjectured in 1994 that the Mobius energy should be minimized, among the class of all nontrivial links in Euclidean space, by the stereographic projection of the standard Hopf link. We prove this conjecture using the min-max theory of minimal surfaces.