arXiv preprints from January 1, 2026 through September 22, 2026 — 11:28:57 EST
We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It is obtained by gluing an algebraic realization of the non-Fano matroid to a realization of the Fano matroid. Its dual is shown not to be algebraic using...
Data-consistent inversion (DCI) constructs probability measures whose push-forward distributions agree with observed data, while iterative data-consistent inversion (iDCI) extends this framework to generalized stochastic inverse problems by enforcing multiple push-forward constraints sequentially. Although iDCI avoids the direct...
The divisible sandpile on $\mathbb{Z}^d$ starts from i.i.d. masses at each site, and, in each discrete time step, a site with mass above one keeps one unit and sends the excess equally to its neighbors. Levine, Murugan, Peres and Ugurcan (2016) showed that at mean one this process explodes, with every site emitting infinite mass. We...
Let $R$ be a discrete valuation ring. We prove that every proper flat finitely presented commutative $R$-group scheme $P$ fits into an exact sequence \[ 0\longrightarrow E\longrightarrow P\longrightarrow B\longrightarrow0, \] where $E$ is finite flat and $B$ is an abelian scheme. For a quasiabelian model---that is, a proper flat...
We study the category of dual operator spaces equipped with an action of a locally compact quantum group $\mathbb{G}$. The Fubini crossed product functor $-\rtimes^\mathcal{F} \mathbb{G}$ and the weak$^*$-crossed product functor $-\bar{\rtimes}\mathbb{G}$ are shown to be equal if and only if $\mathbb{G}$ has the approximation property...
In the parking model, each site of the $d$-dimensional lattice independently starts with one car with probability $p$ or one parking spot with probability $1-p$. Cars move according to independent discrete-time simple random walks and park at the first spot they find free. We prove that in the critical regime $p=1/2$, the expected...
Modern portfolio management increasingly demands a balance between traditional risk-adjusted returns and strict Environmental, Social, and Governance (ESG) mandates. Current Reinforcement Learning (RL) approaches typically optimize for a single ESG provider, neglecting the significant divergence in rating methodologies across the...
Trade durations in high-frequency foreign exchange data exhibit increased occurrence near integer values. To address this empirical phenomenon, we propose the granularity-adjusted autoregressive conditional duration (GA-ACD) model. It is based on a novel two-component mixture distribution consisting of a standard generalized gamma...
This paper develops uniform inference and certified capacity decisions for an estimated financial stability boundary. Conditional risk, temporary cross-impact, and effective risk-bearing capacity are jointly estimated from dependent observations. Conventional pointwise inference is reliable at a separated simple spectral root but can...
This paper develops a mechanism through which costly changes in the representations used for portfolio choice can contribute to persistent signed order flow. Heterogeneous switching thresholds and opportunity volatility generate heterogeneous residence times, and renewal aggregation maps their execution-weighted tail into the decay of...
Transient impact models compose a nonlinearity with a memory kernel, and the order of composition determines the criterion for absence of price manipulation. We classify both orders. If an arbitrary instantaneous law $f$ acts on the trading rate before any nonzero integrable Volterra kernel, nonnegative cost on every finite...
We study a parabolic obstacle partial integro-differential equation (PIDE) with a dynamically moving bilateral free boundary. This type of problem arises in the mathematical modeling of speculative asset bubbles with Lévy jump processes. We consider the existence of viscosity supersolutions within the class of functions exhibiting...
We study deep hedging in the context of dynamics risk measures, where sequential decisions are time-consistent. Whereas the literature in such context mainly considers low-dimensional problems with simple environment dynamics, we tackle the high-dimensional problem of basket option hedging; we show that the approach is feasible and...
Market-order flow in financial markets exhibits long-range correlations. This is a widely known stylised fact of financial markets. A popular hypothesis for this stylised fact comes from the Lillo-Mike-Farmer (LMF) order-splitting theory. However, quantitative tests of this theory have historically relied on proprietary datasets with...
Claims of the form "we find no evidence that X affects Y" appear throughout the applied finance literature, yet whether such a claim contains evidence of absence or absence of evidence depends entirely on its confidence interval. The term "statistically insignificant" is routinely read to mean zero economic effect. However, a more...
The brain is highly proficient at making sense of noisy and ambiguous sensory inputs. Predictive processing hypothesises that this ability relies on prediction. However, it is unclear why the brain would have evolved to predict the sensory world, a computationally expensive process, in order to aid perception. Here we use simulations...
Ultrasound is increasingly used to control biological cells, but its multiple physical effects, including radiation force, streaming, heating, and cavitation, require theoretical frameworks that can quantify their relative strengths. Here we develop a semi-analytical model to predict flow patterns and energy distributions of...
Bayesian phylogenetic and phylodynamic analyses can be very time-consuming, owing to the combination of complex models that are used to estimate key parameters from increasingly large genomic data sets and their associated metadata. The use of high-performance computer hardware can -- to a certain extent -- alleviate the computational...
Sampling error yields exclusively reactive, non-lesional brain parenchyma in a significant proportion of intracranial biopsies, leaving the underlying disease undiagnosed. We benchmark four pathology foundation models (UNI2-h, Virchow2, Prov-GigaPath, H-optimus-0) as frozen patch encoders within a shared attention-based...
The extracellular matrix (ECM) is a fibrous and dynamic network that plays a critical role in development, homeostasis, and disease. Cells both respond to and remodel the ECM, engaging in a mechanical reciprocity that shapes tissues. To study these interactions, computational models have been developed that simulate either ECM...
Species area curves, which describe the number of species present as a function of area, have long been used to understand biodiversity and inform conservation efforts. While understanding the number of species is important, it leaves out information about the population sizes of each species. In this work, we examine the relationship...
This paper argues that fungal mycelial networks exhibit minimal cognition through memory-integrated adaptive regulation. Drawing on cybernetic and enactivist frameworks, I develop a non-representational account of memory as the organism's capacity to modulate behavior based on temporally extended environmental coupling. I propose four...
Existing cell embedding methods predominantly rely on transcriptomic or proteomic measurements and represent each cell as a holistic entity, thereby overlooking the subcellular localization of individual molecules. Moreover, they rarely incorporate protein structural information, despite its fundamental role in determining molecular...
Digital twin technologies could transform neuroscience and biomedicine by creating predictive computational representations of living organisms. However, most animal digital twins model neural circuits, anatomy, or biomechanics separately rather than integrating the processes that generate behavior. We argue that animal digital twins...
This chapter reconstructs the Hopfield network as a physical theory of memory rather than merely an early neural-network algorithm. It begins with the problem as it stood before 1982-threshold logic, Hebbian association, correlation memories, and recurrent binary networks-and isolates what Hopfield's synthesis added: a dynamical...