arXiv research

New method for ancestral inference in branching processes with random environments.

Study on deep neural networks using branching processes and Mehler's formula.

We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitra…

Develops a machine learning method for parameter estimation in branching processes models.

We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data. The method we propose greatly simpli…

Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The field's progression is hampered by the lack of robust software to estimate the numerous parameters of the…

A new algorithm optimizes Gaussian process posterior mean functions efficiently.

This paper models stock prices using a Janardan Galton Watson process.

New method for global optimization of Gaussian processes reduces computational time.

Thanks to the access to labeled orders on the Cac40 index future provided by Euronext, we are able to quantify market participants contributions to the volatility in the diffusive limit. To achieve this result we leverage the branching properties of Hawkes point processes. We find that fast intermediaries (e.g., market…

Gradient estimation techniques applied to programs with randomness in high energy physics.

We introduce a class of interest rate models, called the $α$-CIR model, which gives a natural extension of the standard CIR model by adopting the $α$-stable L{é}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign …

StrTransformer recovers sources without labels by optimizing latent matrices and enforcing structural constraints.

Automated multi-task learning algorithm that optimizes network topology.

First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space $R_+ \times R^d$. We specialize our result to one-dimensional continuous state branching processes with immigration. As an application, we study the asymptotic behavior of least squares estimators…

Unified GP model optimizes hyperparameters with conditional dependence.

We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We…

Branching Flows generates sequences of varying lengths using binary trees.

A GPU framework speeds up BnB for discrete optimization problems.

Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent $H=1/4$. Biase…

The deployment of deep neural networks in real-world applications is mostly restricted by their high inference costs. Extensive efforts have been made to improve the accuracy with expert-designed or algorithm-searched architectures. However, the incremental improvement is typically achieved with increasingly more expen…

VLBM learns MDP transitions from limited data, improving OPE performance.

Study on moduli spaces of branched projective structures on surfaces.

We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are…

New criterion for branched covers between 2-spheres.

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected close surface N with Euler's characteristic less than or equal to 0. This …

New learnability criteria for non-iid processes equivalent to online learning.

Uniformly branching trees are equivalent to certain metric spaces.

The paper studies which branched covers can be lifted to braided embeddings.

We consider 3-dimensional pseudo-manifolds M with a given set of marked point V such that M-V is the interior of a compact 3-manifold with boundary. An ideal triangulation T of (M, V ) has V as its set of vertices. A branching (T, b) enhances T to a Delta-complex. Branched triangulations of (M, V ) are considered up to…

The paper details folding of branched covers of the 3-sphere over knots.

In this work we characterize branch data of branched coverings of even degree over the projective plane which are realizable by indecomposable branched coverings.

Course on knots using branched coverings.

In this note we find a formula for the supremum distribution of spectrally positive or negative Lévy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two branches of the same company) divide between them both claims and premia in some specifie…

This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of age pyramid which evolves according to immigration and births. The virtue if t…

A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot $F$, where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram of $F$. We can simplify a branched cover…

Techniques for constructing codimension 2 embeddings and immersions of the 2 and 3-fold branched covers of the 3 and 4-dimensional spheres are presented. These covers are in braided form, and it is in this sense that they are folded. More precisely the composition of the embedding (or immersion) and the canonical proje…

Formula compares metrics on branched coverings of line bundles.

A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three.

New examples show transverse knots are determined by their branched covers.

We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubble-moves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum Invariants.

Quantized Coulomb branches linked to skein algebras.

Characterizes groups of branched twist-spun knots.

We prove that if S is a closed compact surface of negative Euler characteristic, and if R is a quasi-Fuchsian representation in PSL(2,C), then the deformation space M(k,R) of branched projective structures on S with total branching order k and holonomy R is connected, as soon as k>0. Equivalently, two branched projecti…

We provide criteria ensuring that a tunnel number one knot $K$ is not determined by its double branched cover, in the sense that the double branched cover is also the double branched cover of a knot $K'$ not equivalent to $K$.

Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constraints can be realized by some branched cover. We connect recent development in spherical conic metrics to this old problem, and give a new m…

Authors prove a contact structure result using branched covers and overtwisted disks.

For any alternating knot, it is known that the double branched cover of the $3$-sphere branched over the knot is an $L$-space. We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.