### Introduction to Solving Quant Finance Problems with Time-Stepped FBSDE and Deep Learning. (arXiv:1911.12231v1 [q-fin.CP])

In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic differential equations (FBSDE) final-value or control problems, how these final value problems can be turned into control problems, how time-continuous problems can be turned…

### Estimation and simulation of the transaction arrival process in intraday electricity markets. (arXiv:1901.09729v3 [econ.GN] UPDATED)

We examine the novel problem of the estimation of transaction arrival processes in the intraday electricity markets. We model the inter-arrivals using multiple time-varying parametric densities based on the generalized F distribution estimated by maximum likelihood. We analyse both the in-sample characteristics and the probabilistic forecasting performance. In a rolling window forecasting study, we simulate…

### A Markovian genomic concatenation model guided by persymmetric matrices. (arXiv:1805.02231v2 [q-bio.GN] UPDATED)

The aim of this work is to provide a rigorous mathematical analysis of a stochastic concatenation model presented by Sobottka and Hart (2011) which allows approximation of the first-order stochastic structure in bacterial DNA by means of a stationary Markov chain. Two probabilistic constructions that rigorously formalize the model are presented. Necessary and sufficient conditions…

### Breakdown of effective temperature, power law interactions and self-propulsion in a momentum conserving active fluid. (arXiv:1808.03091v3 [cond-mat.soft] UPDATED)

Simplest extensions of single particle dynamics in momentum conserving active fluid – that of an active suspension of two colloidal particles or a single particle confined by a wall – exhibit strong departures from Boltzmann behavior, resulting in either a breakdown of an effective temperature description or a steady state with nonzero entropy production rate.…

### Classes of treebased networks. (arXiv:1810.06844v4 [q-bio.PE] UPDATED)

Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the base tree, by adding additional edges. The main aim of this manuscript is to provide some sufficient criteria for treebasedness by reducing phylogenetic networks to related…

### Embeddability and rate identifiability of Kimura 2-parameter matrices. (arXiv:1902.08555v2 [q-bio.PE] UPDATED)

Deciding whether a Markov matrix is embeddable (i.e. can be written as the exponential of a rate matrix) is an open problem even for $4\times 4$ matrices. We study the embedding problem and rate identifiability for the K80 model of nucleotide substitution. For these $4\times 4$ matrices, we fully characterize the set of embeddable K80…

### DNA energy constraints shape biological evolutionary trajectories. (arXiv:1905.00621v2 [q-bio.BM] UPDATED)

Most living systems rely on double-stranded DNA (dsDNA) to store their genetic information and perpetuate themselves. This biological information has been considered the main target of evolution. However, here we show that symmetries and patterns in the dsDNA sequence can emerge from the physical peculiarities of the dsDNA molecule itself and the maximum entropy principle…

### Intrinsic noise, Delta-Notch signalling and delayed reactions promote sustained, coherent, synchronised oscillations in the presomitic mesoderm. (arXiv:1906.09236v2 [q-bio.SC] UPDATED)

Using a stochastic individual-based modelling approach, we examine the role that Delta-Notch signalling plays in the regulation of a robust and reliable somite segmentation clock. We find that not only can Delta-Notch signalling synchronise noisy cycles of gene expression in adjacent cells in the presomitic mesoderm (as is known), but it can also amplify and…

### Integral Remez inequalities for polynomials on convex bodies. (arXiv:1911.11878v1 [math.FA])

We denote as an integral Remez inequality an inequality of the form $$\|f\|_{L^{1}(\mu)} \le C(\Omega,\mu(A), X) \|f\|_{L^{1}(\mu_{A})},$$ where $\mu_A$ is the normalised restriction of a measure $\mu$ to a set $A$. Let $\mu$ be the uniform distribution over a convex body A and $f$ be a polynomial of degree $d$. One can choose…

### Bounding Zolotarev numbers using Faber rational functions. (arXiv:1911.11882v1 [math.CV])

By closely following a construction by Ganelius, we construct Faber rational functions that allow us to derive tight and explicit bounds on Zolotarev numbers.