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.
The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.
The paper characterizes global hyperbolicity in Lorentzian manifolds without relying on manifold topology.
Diamonds help compute volatility models efficiently.
Study of circle homeomorphisms with square summable diamond shears.
Develops a diamond price index for online auction platforms.
Study defines new products for Lorentzian spaces and analyzes causal diamonds.
Soft diamond regularizers improve deep learning performance and sparsity.
We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of th…
Chronological Causal Bandits (CCB) tackles dynamic causal decision-making.
IMPaCT improves node classification in chronological split temporal graphs.
Chronologically consistent models maintain accuracy with time-restricted data.
New tool helps classify invariant subvarieties in degenerations.
The geometry of causal diamonds or Alexandrov open sets whose initial and final events and respectively have a proper-time separation small compared with the curvature scale is a universal. The corrections from flat space are given as a power series in whose coefficients involve the curvature at the cen…
Diamond method controls FDR for trustworthy feature interaction discovery in ML models.
Paper introduces a new convergence for Lorentzian spaces using causal diamonds.
New models avoid lookahead bias by training on past data only.
Generalizes global hyperbolicity to higher signatures and proves compactness.
Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.
The paper resolves kinks on curves on surfaces with punctures.
In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property…
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the red-shift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction and it takes its maximal value at the cen…
We solve a lifecycle model in which the consumer's chronological age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate in time like a broken clock that might occasionally move backwards. In other words, biological age could actually decline. Our paper is ins…
A new method extracts features from time series data using iterated sums and improves classification accuracy.
A 3-manifold is foliar if it supports a codimension-one co-oriented taut foliation. Suppose is an oriented 3-manifold with connected boundary a torus, and suppose contains a properly embedded, compact, oriented, surface with a single boundary component that is Thurston norm minimizing in $H_2(M, \partial M)…
Chronnet models spatiotemporal data using chronological networks.
Recently, the intervention calculus when the DAG is absent (IDA) method was developed to estimate lower bounds of causal effects from observational high-dimensional data. Originally it was introduced to assess the effect of baseline biomarkers which do not vary over time. However, in many clinical settings, measurement…
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causal…
Defines a geometric dimension for Lorentzian spaces, distinguishing spacelike and null subspaces.
In a previous paper we obtained formulae for the volume of a causal diamond or Alexandrov open set whose duration is short compared with the curvature scale. In the present paper we obtain asymptotic formulae valid when the point recedes to the future boundary of an asymp…
We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms al…
Reconstruct spacetime from order and number of points.
The paper examines how timing of observations affects causal discovery methods.
Study on Hausdorff dimension and curvature bounds in sub-Lorentzian Heisenberg group.
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are not included, and things are not presented in chronological order.
The study proves timelike Ricci bounds for low regularity spacetimes using optimal transport.
New curvature measure for causal sets derived from optimal transport.
There are two categorifications of the Jones polynomial: "even" discovered by M.Khovanov in 1999 and "odd" dicovered by P.Ozsvath, J.Rasmussen and Z.Szabo in 2007. The first one can be fully constructed in the category of cobordisms (strictly: in the additive closure of that category), where we can build a complex for …
Comparing data defined over space and time is notoriously hard, because it involves quantifying both spatial and temporal variability, while at the same time taking into account the chronological structure of data. Dynamic Time Warping (DTW) computes an optimal alignment between time series in agreement with the chrono…
We show that K3 surfaces with non-symplectic automorphisms of prime order can be used to construct new compact irreducible G2-manifolds. This technique was carried out in detail by Kovalev and Lee for non-symplectic involutions. We use Chen-Ruan orbifold cohomology to determine the Hodge diamonds of certain complex thr…
Researchers examine various causal structures for spacetimes with continuous metrics.
There are various algorithms and methodologies used for automated screening of cervical cancer by segmenting and classifying cervical cancer cells into different categories. This study presents a critical review of different research papers published that integrated AI methods in screening cervical cancer via different…
Constructs minimal surfaces over Pitot quadrilaterals using harmonic diffeomorphisms.
Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are define…
For any positive integer m and any dimension n, we show that any n-dimensional Hodge diamond with values in Z/mZ is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective va…
We study properties of the mean curvature one-form and its holomorphic and antiholomorphic cousins on a transverse Kähler foliation. If the mean curvature of the foliation is automorphic, then there are some restrictions on basic cohomology similar to that on Kähler manifolds, such as the requirement that the odd basic…
Estimates financial market impacts of COVID-19 using time-varying kernel density.
In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. However, one might wonder whether the corresponding incomplete geodesics could still …
We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metrics, while retaining all of the equivalences to other notions of global hyperbolicity. In fact, global hyperbolicity is equivalent to the co…