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.
Unified framework for strain-gradient plasticity from dislocations.
We reconcile between two classical models of edge-dislocations in solids. The first model, dating from the early 1900s models isolated edge-dislocations as line singularities in locally-Euclidean manifolds. The second model, dating from the 1950s, models continuously-distributed edge-dislocations as smooth manifolds en…
Study of knotted defects in smectic liquid crystals using topological knot theory.
We present a rigorous homogenization theorem for distributed dislocations. We construct a sequence of locally-flat Riemannian manifolds with dislocation-type singularities. We show that this sequence converges, as the dislocations become denser, to a flat non-singular Weitzenböck manifold, i.e. a flat manifold endowed …
Large twist-angle grain boundaries in layered structures are often described by Scherk's first surface whereas small twist-angle grain boundaries are usually described in terms of an array of screw dislocations. We show that there is no essential distinction between these two descriptions and that, in particular, their…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
Using the most comprehensive, commercially-available dataset of trading activity in U.S. equity markets, we catalog and analyze quote dislocations between the SIP National Best Bid and Offer (NBBO) and a synthetic BBO constructed from direct feeds. We observe a total of over 3.1 billion dislocation segments in the Russ…
This note refers to our previous paper "The emergence of torsion in the continuum limit of distributed edge-dislocations". It identifies and fixes an error in the notion of convergence of Weitzenböck manifolds defined in the paper, and in the proof of the well-definiteness of this notion of convergence.
The 1950's foundational literature on rational mechanics exhibits two somewhat distinct paradigms to the representation of continuous distributions of defects in solids. In one paradigm, the fundamental objects are geometric structures on the body manifold, e.g., an affine connection and a Riemannian metric, which repr…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, . We prove the -convergence of elastic energies for configurations of a converging sequence, , of body manifolds. This convergence result …
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other …
We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We then consider the static case, which describes crystalline bodies in equilibriu…
We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two des…
Analyzes news graphs to predict financial market dislocations.
Using the most comprehensive source of commercially available data on the US National Market System, we analyze all quotes and trades associated with Dow 30 stocks in 2016 from the vantage point of a single and fixed frame of reference. We find that inefficiencies created in part by the fragmentation of the equity mark…
Theory of space-time currents for geometric evolutions.
Motivated by the importance and universal character of phase singularities which are clarified recently, we study the local structure of equi-phase loci near the dislocation locus of complex valued planar and spatial waves, from the viewpoint of singularity theory of differentiable mappings, initiated by H. Whitney and…
This expository paper is a tribute to Ekkehart Kröner's results on the intrinsic non-Riemannian geometrical nature of a single crystal filled with point and/or line defects. A new perspective on this old theory is proposed, intended to contribute to the debate around the still open Kröner's question: "what are the dyna…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a configuration of a body in classical elasticity is the sum of local contributions …
The goal of this paper is twofold. First we prove a rigidity estimate, which generalises the theorem on geometric rigidity of Friesecke, James and Müller to 1-forms with non-vanishing exterior derivative. Second we use this estimate to prove a kind of spontaneous breaking of rotational symmetry for some models of cryst…
Study on materials with disclinations, limiting their size.
Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and applications. Given any material property, such as the elastic energy or an inde…
Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or e…
The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the intera…
We present a general derivation of the arbitrage-free pricing framework for multiple-currency collateralized products. We include the impact on option pricing of the policy adopted to fund in foreign currency, so that we are able to price contracts with cash flows and/or collateral accounts expressed in foreign currenc…
Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By emphasizing the geometric nature of such anomalies we seek their representation…
Generalizes beam models to include curvature and torsion.
Abstract framework for cross-currency interest rate contracts.
New techniques identify shifts in financial market sectors.
Study finds short-term trading signals can enhance alpha in U.S. S&P 500 portfolios.
Endoscopic diagnosis is an important means for gastric polyp detection. In this paper, a panoramic image of gastroscopy is developed, which can display the inner surface of the stomach intuitively and comprehensively. Moreover, the proposed automatic detection solution can help doctors locate the polyps automatically, …
A new model for defective media using two scales.