arXiv research

We consider a disk-shaped thin elastic sheet bonded to a compliant sphere. (Our sheet can slip along the sphere; the bonding controls only its normal displacement.) If the bonding is stiff (but not too stiff), the geometry of the sphere makes the sheet wrinkle to avoid azimuthal compression. The total energy of this sy…

Generates music with coherent rhythm, chords, and melody using LSTM models.

Model shows how banks' hidden-to-maturity accounting can mask run risk and lead to financial instability.

New deep learning method improves financial stress testing accuracy.

A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing individual banks; associated with each node is a balance sheet consisting of assets and …

A world sheet in anti-de Sitter space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds. We consider the family of lightlike hypersurfaces along spacelike submanifolds in the world sheet. The locus of the singularities of lightlike hypersurfaces along spacelike submanifolds forms …

In the Minkowski space-time, a world hyper-sheet is a timelike hypersurface consisting of a one-parameter family of spacelike submanifolds. Recently, Bousso and Randall introduced the notion of caustics of world hyper-sheets in order to define the notion of holographic domains in space-time. Here, we give a mathematica…

Paper tackles score following in full-page sheet music images.

A world sheet in Lorentz-Minkowski space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds in Lorentz-Minkowski space. In this paper we investigate differential geometry of world sheets in Lorentz-Minkowski space as an application of the theory of big wave fronts.

Study compares empirical systemic risk with balance sheet risk in interbank networks.

This systemic risk paper introduces inhomogeneous random financial networks (IRFNs). Such models are intended to describe parts, or the entirety, of a highly heterogeneous network of banks and their interconnections, in the global financial system. Both the balance sheets and the stylized crisis behaviour of banks are …

This paper finds a new method for decomposing insurer profits and losses.

Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $Φ(c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly s…

A new XVA strategy rooted in balance sheet perspective improves equity process for bank shareholders.

The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip a…

Weakly stable constant mean curvature (CMC) hypersurfaces are stable critical points of the area functional with respect to volume preserving deformations. We establish a pointwise curvature estimate (in the non-singular dimensions) and a sheeting theorem (in all dimensions) for weakly stable CMC hypersurfaces, giving …

In this fact sheet we give some preliminary research results on the Bayesian Decision Theory. This theory has been under construction for the past two years. But what started as an intuitive enough idea, now seems to have the makings of something more fundamental.

The goal of score following is to track a musical performance, usually in the form of audio, in a corresponding score representation. Established methods mainly rely on computer-readable scores in the form of MIDI or MusicXML and achieve robust and reliable tracking results. Recently, multimodal deep learning methods h…

We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and deri…

This paper shows how to create surface-links with many triple points.

Novel defects in hyperbolic sheets explain complex wrinkling patterns in nature.

This paper shows how to construct anomaly free world sheet actions in string theory with $D$-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to $D$-branes and connections on them. The holonomy of these connections can be used to cancel g…

The paper studies quandles over a hyperboloid and computes a knot invariant.

The paper classifies ovals in 4D space for a specific flow.

We prove that if $M \longrightarrow P$ is a small cover of a compact right-angled hyperbolic polyhedron $P$ then $M$ admits a cofinal tower of finite sheeted covers with positive rank gradient. As a corollary, if $π_1(M)$ is commensurable with the reflection group of $P$, then $M$ admits a cofinal tower of finite sheet…

A combinatorial presentation of closed orientable 3-manifolds as bi-tricolored links is given together with two versions of a calculus via moves to manipulate bi-tricolored links without changing the represented manifold. That is, we provide a finite set of moves sufficient to relate any two manifestations of the same …

New geometric theory explains nonuniform origami responses.

Torus covers have controlled volume and diameter under curvature and diameter bounds.

We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in $α'$ in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we…

This paper compiles and calculates triple point numbers for surface-links in Yoshikawa's table.

It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such solution its reciprocal is the radial function of only one o…

Worldsheet wraps a 3D mesh sheet onto a single image to synthesize novel views.

In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distrib…

Kirigami-inspired math reveals shortest paths and ultimate shapes of cut paper.

The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a ver…

The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology (i) emerges even in zero strain configurations, and (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key…

Neural-network emulators predict sea-level changes due to Antarctic ice melt.

In this note we clarify the relation between extended world-sheet supersymmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism between the group of orthogonal automorphisms of the Courant bracket and the group…

Model predicts insolvency risks in banks due to liquidity and credit risks.

New method allows sheets to morph into multiple shapes via spatially varying stimuli.

We consider the Blum medial axis of a region in $\mathbb R^n$ with piecewise smooth boundary and examine its "rigidity properties", by which we mean properties preserved under diffeomorphisms of the regions preserving the medial axis. There are several possible versions of rigidity depending on what features of the Blu…

A holomorphic Poisson structure induces a deformation of the complex structure as Hitchin's generalized geometry. Its associated cohomology naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is the Dolbeault cohomology with coefficients in the exterior a…

Model shows bailout stigma affects firm funding and market performance.

We construct an invariant of parametrized generic real algebraic surfaces in RP^3 which generalizes the Brown invariant of immersed surfaces from smooth topology. The invariant is constructed using the self intersection, which is a real algebraic curve with points of three local characters: the intersection of two real…

Study on vortex sheet formation in Abelian gauge theories.

We present a Hamiltonian framework for higher-dimensional vortex filaments (or membranes) and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively, i.e. singular elements of the dual to the Lie algebra of divergence-free vector fields. It turns out that the localized induction approximat…

We consider a model of contagion in financial networks recently introduced in the literature, and we characterize the effect of a few features empirically observed in real networks on the stability of the system. Notably, we consider the effect of heterogeneous degree distributions, heterogeneous balance sheet size and…

Study shows torsion grows subexponentially in book of I-bundles but can grow exponentially in non-regular covers.