Proposes a method to predict both time and mark of next event in marked temporal dynamics.
problem Predicting both time and mark of the next event in marked temporal dynamics.
method Uses a mark-specific intensity function to model the dependency between time and mark.
result Outperforms state-of-the-art methods in predicting marked temporal dynamics.
New model captures time and mark inter-dependence in TPPs.
problem Limited predictive performance of conditionally independent TPP models on entangled time and mark interactions.
method Developed a multivariate TPP that models conditional inter-dependence of time and mark, using both intensity-based and intensity-free models.
result Proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks.
Methodology for estimating marked Hawkes processes with neural networks.
problem Estimating conditional intensity of marked Hawkes processes.
method Proposes two models: Shallow Neural Hawkes with marks and Neural Network for Non-Linear Hawkes with Marks.
result Validation on synthetic datasets and real-world cryptocurrency order book data.
Over-the-counter derivatives have contributed significantly to the effectiveness and efficiency of the international financial system but also entail significant counterparty credit risk. Collateralization is one of the most important and widespread credit risk mitigation techniques used in derivatives transactions. Ho…
Neural marked point processes show saturation with complexity, leading to new simple architectures.
problem Performance saturation in neural marked point processes with complex architectures.
method Proposed GCHP with graph convolutional layers and likelihood ratio loss.
result GCHP reduces training time and improves model performance.
A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.
problem Pricing derivatives with accumulated marks using a self-exciting marked point process.
method Derive discounted pricing equation as a PIDE, transform to one-dimensional PIDEs, use Laplace/Fourier transform, approximate jump term, solve using finite difference scheme.
result Efficiently price derivatives with accumulated marks using a novel finite-difference and transform approach.
The purpose of this paper is to design an algorithm for the computation of the counterparty risk which is competitive in regards of a brute force "Monte-Carlo of Monte-Carlo" method (with nested simulations). This is achieved using marked branching diffusions describing a Galton-Watson random tree. Such an algorithm le…
Introduces a new class of hybrid processes combining Markov chains and Hawkes processes.
problem Characterize and ensure existence and uniqueness of complex hybrid marked point processes.
method Defines hybrid marked point processes implicitly via intensity and state process interactions, proving existence and uniqueness under general assumptions.
result Proves existence and uniqueness of hybrid marked point processes, extending existing results.
This paper tackles efficient learning for factorial marked temporal point processes.
problem Efficient learning for factorial marked temporal point processes.
method Decoupled learning method with two procedures: ADM-M and Fast ISTA, and a reformulated Logistic Regression model.
result Empirical results show the efficiency of the decoupled and reformulated method.
Algorithms compute length spectra of torus graphs efficiently.
problem Computing length spectra of graphs embedded on a torus.
method Preprocessing and algorithms based on polyhedral norms.
result Efficient computation of length spectra and spectrum comparison.
New method recalibrates VaR for option books, reducing forecast errors.
problem Inaccurate VaR forecasts due to missing operational choices.
method Marking-aware sequential VaR recalibration targeting normalized book-level loss.
result Sequential VaR recalibration improves VaR performance across different markets and options.
We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider's information flow by us…
The authors seek financial datasets to benchmark feature engineering methods on US market data.
problem Improving predictive models for financial data science competitions.
method Feature engineering methods applied to multivariate time-series data from the US market.
result Predictive power of models tested against Numerai-Signals targets.
New method models MTPP without predefined intensity functions.
problem Parameterizing conditional joint PDF for MTPP.
method IFIB framework, modeling p∗(m,t) directly. result Superior experimental results on real and synthetic data.
We present a marked analogue of Carter and Saito's movie theorem. Our definition of marking was chosen to coincide with the markings that arise in link Floer homology. In order to deal with complications arising from certain isotopies, we define three equivalence relations for marked surfaces and work over an equivalen…
Study applies Hawkes volatility to mid-price process for real-time risk management.
problem Lack of studies on Hawkes volatility for tick-level price dynamics.
method Derived variance formula for unmarked and marked Hawkes models, applied to mid-price process.
result Reliable results and high predictive power of intraday Hawkes volatility.
Classifies markings on translation surfaces from covering constructions.
problem Understanding point markings on translation surfaces.
method Branched covering constructions and periodic points.
result Complete classification of point markings over strata of quadratic differentials.
A marked graph diagram is a link diagram possibly with marked 4-valent vertices. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of representing surface-links by marked graph diagrams. Specially, K. Yoshikawa gave local moves on marked graph diagrams, nowadays called Yoshikawa moves. It is now known that two…
New model for multivariate discrete event data with flexible interactions.
problem Modeling multivariate discrete event data with categorical interactions.
method Developed a new modeling approach with convex constraints, two estimation procedures (LS and ML).
result Proposed model can capture arbitrary shapes of historical event influence.
Survey on decorated marked surfaces for Calabi-Yau categories.
problem Understanding Calabi-Yau categories and related structures.
method Introducing decorations on marked surfaces to study various categories.
result Exploration of Calabi-Yau-2 and 3 categories, braid groups, quadratic differentials, and stability conditions.
Study of skein modules of marked 3-manifolds and Chebyshev-Frobenius homomorphism.
problem Understanding skein modules of marked 3-manifolds and their algebraic properties.
method Extension of Muller's result to marked surfaces with unmarked boundary components, development of surgery theory, and application of Chebyshev homomorphism.
result Extension of Chebyshev-Frobenius homomorphism to skein modules of marked 3-manifolds and characterization of its image.
Predict cell loads in cellular networks using statistical learning of geometric marks.
problem Predicting cell loads in cellular networks using geometric marks.
method Statistical regression model and scattering moments of random measures.
result Scattering moments can capture similar geometry information as baseline approach and improve performance.
Study approximate marked length spectrum rigidity in non-positively curved groups.
problem Approximate rigidity of marked length spectra in non-positively curved groups.
method Compare marked length spectra of isometric actions of groups with non-positively curved features.
result Supremum of quotient of marked length spectra is approximately determined by restricted spectra.
We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the hyperelliptic involution. We show that these point markings can be used to determin…
Differentiable adversarial attacks improve model robustness in MTPP models.
problem Improving model robustness against adversarial attacks in MTPP models.
method Proposed a differentiable adversarial attack scheme PERMTPP that addresses the sequential nature and varying time-scales of MTPPs.
result Demonstrated offensive and defensive capabilities, and reduced inference times on real-world datasets.
Paper tackles reinforcement learning for asynchronous events.
problem Designing online interventions for complex asynchronous environments.
method Deep reinforcement learning of marked temporal point processes.
result Method can find effective interventions for diverse applications.
We use Fox calculus to assign a marked polytope to a `nice' group presentation with two generators and one relator. Relating the marked vertices to Novikov-Sikorav homology we show that they determine the Bieri-Neumann-Strebel invariant of the group. Furthermore we show that in many cases the marked polytope is an inva…
Quantum duality map extended to general marked surfaces and its compatibility with skein algebras proven.
problem Generalizing quantum duality map to general marked surfaces and proving its compatibility with skein algebras.
method Generalized quantum duality map, reduced stated skein algebras, quantum trace maps, skein lifting.
result Compatibility of quantum duality map with skein algebras proven.
Paper shows non-arithmetic surface with unique geometric property.
problem Non-arithmetic surfaces with unique geometric properties.
method Example of a non-arithmetic surface with marked length variety rigidity.
result Found a non-arithmetic surface with marked length variety rigidity.
A new mosaic system for immersed surface-links is introduced.
problem Constructing a mosaic system for immersed surface-links.
method Using singular marked graph diagrams, the mosaic number for immersed surface-links is defined and discussed.
result A mosaic system for immersed surface-links is established.
New stability estimate for Anosov manifolds' metrics.
problem Locally determine the metric from the marked length spectrum.
method Anosov geodesic flow and non-positive curvature.
result Two close enough metrics with the same marked length spectrum are isometric.
Classifies foliated complex manifolds using marked fans.
problem Understanding foliated complex manifolds similar to toric varieties.
method Classifies by marked fans and describes cohomology algebras.
result Basic cohomology and Dolbeault cohomology algebras described in terms of marked fans.
A new method uses Brownian motion local time to estimate counterparty risk efficiently.
problem Efficient estimation of counterparty risk in OTC derivatives contracts.
method Exploiting properties of Brownian motion local time to compute risk.
result Significantly reduces computational effort and costs in estimating counterparty risk.
A graph helps understand Artin groups better.
problem Understanding the structure of Artin groups.
method Constructing a marking graph with transverse parabolic subgroups and defining natural moves.
result The marking graph is quasi-isometric to the group modulo its center.
Paper extends method of presenting surface-links to immersed surface-links.
problem Presenting immersed surface-links in 4-space.
method Use marked graph diagrams with moves preserving isotopy classes.
result Extended method for presenting immersed surface-links.
The paper constructs a moduli space for opers and proves its symplectic properties.
problem Understanding the moduli space of opers and its symplectic structure.
method Constructing the moduli space of marked oper structures and proving properties of the holonomy map.
result The symplectic structure on the moduli space of marked complex projective structures extends to a pre-symplectic structure on the moduli space of marked opers.
Survey of stated skein modules/algebras of 3-manifolds/surfaces.
problem Understanding stated skein modules/algebras of 3-manifolds/surfaces.
method Discussion of splitting homomorphism, general structures, Frobenius homomorphism, center, dimension, representation theory.
result Skein algebra of non-closed marked surface at any root of 1 is a maximal order.
New Khovanov homology for marked links collapses spectral sequence.
problem Understanding instanton theory and its relation to Khovanov homology.
method Introducing marked Khovanov homology and studying its properties.
result Khovanov homology for alternating links does not depend on marking data for non-split links.
New rigidity result for convex co-compact actions in products of spaces.
problem Rigidity of convex co-compact actions in products of spaces.
method Analyzing diagonal actions and marked length spectra.
result If a diagonal action is convex co-compact, then the individual actions have the same marked length spectrum.
Develops quasi-likelihood analysis for marked point processes and applies it to Hawkes processes.
problem Analyzing multivariate marked point processes and their applications.
method Quasi-likelihood analysis for a general class of multivariate marked point processes, with focus on marked Hawkes processes.
result The quasi-likelihood analysis for marked Hawkes processes provides explicit conditions for ergodicity and Markovian transformation.
The paper extends intensity models for limit order books using marked point processes.
problem Modeling intensity ratios in limit order books with state dependency and clustering.
method Developed a new model combining three multiplicative components for marked point processes.
result The new model outperforms other intensity-based methods in predicting market order signs and aggressiveness.
We prove that the classical set of moves for standard spines of 3-manifolds (i.e. the MP-move and the V-move) does not suffice to relate to each other any two standard skeleta of a 3-manifold with marked boundary. We also describe a condition on the 3-manifold with marked boundary that tells whether the generalised set…
Study of infinite type surfaces' mapping class groups via hyperbolic structures.
problem Understanding mapping class groups of infinite type surfaces.
method Definition of a topology on a moduli space of marked hyperbolic structures.
result Continuous action of mapping class groups on the marked moduli space.
A new method uses Transformers for efficient prediction of marked point processes.
problem Efficiently predicting the next event in a sequence given its history.
method Modeling conditional inter-event times with a mixture of log-normals and marks with a Transformer architecture.
result The method achieves state-of-the-art performance and is faster during inference.
Closed manifolds with close marked spectra are approximately isometric.
problem Closed manifolds with close marked length spectra are approximately isometric.
method Using Hamenstädt's methods and Gromov compactness theorem, we show diffeomorphism and volume equality.
result Closed manifolds with close marked spectra are approximately isometric.
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken …
New theorem shows metrics of certain groups are close if their lengths are identical.
problem Identifying metrics of relatively hyperbolic groups from their lengths.
method Proved rigidity for relatively hyperbolic groups using coarse marked length spectrum.
result Metrics of relatively hyperbolic groups are uniformly close if lengths are identical.
Marked vertex diagrams provide a combinatorial way to represent knotted surfaces in R4; including virtual crossings allows for a theory of virtual knotted surfaces and virtual cobordisms. Biquandle counting invariants are defined only for marked vertex diagrams representing knotted orientable surfaces; we e…