arXiv subjects

Benjamin Brindle

Publications and source records attributed to Benjamin Brindle.

7 recordsLinked to original sources

arXiv2026

Language Markers of Emotion Flexibility Predict Depression and Anxiety Treatment Outcomes

Predicting treatment non-response for anxiety and depression is challenging, in part because of sparse symptom assessments in real-world care. We examined whether passively captured, fine-grained emotions serve as linguistic markers of treatment outcomes by analyzing 12 weeks of de-identified teletherapy transcripts from 12,043 U.S. patients with moderate-to-severe anxiety and depression symptoms. A transformer-based small language model extracted patients' emotions at the talk-turn level; a state-space model (VISTA-SSM) clustered subgroups based on emotion dynamics over time and produced temporal networks. Two groups emerged: an improving group (n=8,230) and a non-response group (n=3,813) showing increased odds of symptom deterioration, and lower likelihood of clinically significant improvement. Temporal networks indicated that sadness and fear exerted most influence on emotion dynamics in non-responders, whereas improving patients showed balanced joy, sadness, and neutral expressions. Findings suggest that linguistic markers of emotional inflexibility can serve as scalable, interpretable, and theoretically grounded indicators for treatment risk stratification.

cs.CL↗

arXiv2025

On the structure of Multiple q-Zeta Values

In 2015, Bachmann \cite{Ba3} conjectured that the~$\Q$-vector space~$\Zq$ of (formal)~$q$-analogues of Multiple Zeta Values (\qmzv s) is spanned by a very particular set compared to known spanning sets. In this work, we prove that this conjecture is true for a subspace of~$\Zq$ spanned by words satisfying some condition on their number of zeros and depth. According to this partial result, we give an explicit approach to the whole conjecture, based on particular~$\Q$-linear relations among formal Multiple~$q$-Zeta Values which are implied by duality.

math.NT↗

arXiv2024

VISTA-SSM: Varying and Irregular Sampling Time-series Analysis via State Space Models

We introduce VISTA, a clustering approach for multivariate and irregularly sampled time series based on a parametric state space mixture model. VISTA is specifically designed for the unsupervised identification of groups in datasets originating from healthcare and psychology where such sampling issues are commonplace. Our approach adapts linear Gaussian state space models (LGSSMs) to provide a flexible parametric framework for fitting a wide range of time series dynamics. The clustering approach itself is based on the assumption that the population can be represented as a mixture of a fixed number of LGSSMs. VISTA's model formulation allows for an explicit derivation of the log-likelihood function, from which we develop an expectation-maximization scheme for fitting model parameters to the observed data samples. Our algorithmic implementation is designed to handle populations of multivariate time series that can exhibit large changes in sampling rate as well as irregular sampling. We evaluate the versatility and accuracy of our approach on simulated and real-world datasets, including demographic trends, wearable sensor data, epidemiological time series, and ecological momentary assessments. Our results indicate that VISTA outperforms most comparable standard times series clustering methods. We provide an open-source implementation of VISTA in Python.

stat.AP↗

arXiv2024

Combinatorial interpretation of the Schlesinger-Zudilin stuffle product

We derive an explicit formula for the quasi--shuffle product satisfied by Schlesinger--Zudilin Multiple~$q$-Zeta Values, expressed in terms of partition data. To achieve this, we interpret Schlesinger--Zudilin Multiple~$q$-Zeta Values as generating series of distinguished marked partitions, which are partitions whose Young diagrams have certain rows and columns marked. Together with the description of duality using marked partitions in~\cite{Br2}, and Bachmanns conjecture~(\cite{BaTalk}) that all linear relations among Multiple~$q$-Zeta Values are implied by duality and the stuffle product, this paper completes the description of the conjectural structure of Multiple~$q$-Zeta Values using marked partitions.

math.CO↗

arXiv2023

Asymptotic expansions for partitions generated by infinite products

Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in $\mathcal{L}\subset\mathbb{N}$ ($\gcd(\mathcal{L})=1$) and good analytic properties of the corresponding zeta function, generalizing work of Meinardus. In this paper, we extend their work to prove asymptotic formulas if $\mathcal{L}$ is a multiset of integers and the zeta function has multiple poles. In particular, our results imply an asymptotic formula for the number of irreducible representations of degree $n$ of $\mathfrak{so}{(5)}$. We also study the Witten zeta function $\zeta_{\mathfrak{so}{(5)}}$, which is of independent interest.

math.NT↗

arXiv2021

A unified approach to qMZVs

This survey gives a self-contained introduction to q-analogues of multiple zeta values (qMZVs). For this, we consider most common models of qMZVs in a unified setup going back to Bachmann and K\"uhn, such as a related quasi-shuffle product each. Also, we give distinguished translations between several models. As another unified approach to qMZVs, we introduce the concept of marked partitions.

math.NT↗

arXiv2021

Proving dualities for qMZVs with connected sums

This paper gives a new application of so-called connected sums, introduced recently by Seki and Yamamoto. Special about our approach is that it proves a duality for the Schlesinger-Zudilin and the Bradley-Zhao model of qMZVs simultaneously. The latter implies the duality for MZVs and the former can be used to prove the shuffle product formula for MZVs. Furthermore, the $q$-Ohno relations, a generalization of Bradley-Zhao duality, is also obtained.

math.NT↗