arXiv subjects

Marina Palaisti

Publications and source records attributed to Marina Palaisti.

10 recordsLinked to original sources

arXiv2026

Low-Rank and Sparse Drift Estimation for High-Dimensional Lévy-Driven Ornstein--Uhlenbeck Processes

We study drift estimation for discretely observed high-dimensional Lévy-driven Ornstein--Uhlenbeck processes when the drift admits a low-rank-plus-sparse approximation. A localized, increment-truncated pseudo-likelihood is regularized by nuclear and entrywise $\ell_1$ norms. A weighted joint-cone argument and restricted cancellation condition yield non-asymptotic Frobenius oracle inequalities for exact and approximate structure. The stochastic complexity is $rd+s\log d$, with explicit discretization, truncation, and Lévy-regime sample-complexity terms. We derive operator- and infinity-norm score bounds from a Gaussian-width inequality and give a proximal-gradient algorithm. In 100-replicate experiments with mixed low-rank-plus-sparse drift, the estimator reduces mean relative Frobenius error by 4.4--5.9\% versus localized Lasso and wins 89--92\% of paired paths. Component diagnostics show that these gains concern recovery of the total drift rather than exact identification of its low-rank and sparse components.

math.PR↗

arXiv2026

Marginal Persistence and Dynamic Copula Dependence in Sovereign Rating Migration Counts: A Discrete Interval-Likelihood MAGMAR Analysis

This paper develops an observed-data likelihood for applying moving-aggregate modified autoregressive (MAGMAR) copula time-series models to discrete sovereign rating-migration counts with time-varying exposure. An annual count identifies a probability-integral-transform interval rather than a unique latent point, so the likelihood integrates the latent process over the complete sequence of count intervals. A guided sequential Monte Carlo implementation incorporates the parameter-dependent stationary marginal adjustment of MAGMAR directly inside this integration. In sovereign ratings from Fitch, Moody's, and S\&P over 1963--2025, the migration counts are strongly overdispersed relative to a binomial margin and, under an exposure-conditioned static beta-binomial margin, MAGMAR improves substantially on MAG. The interpretation changes once the marginal mean is allowed to depend on the lagged migration rate: residual serial correlation in the count margin disappears, a reference dynamic-margin fit gives only a small MAGMAR improvement, and information criteria favor MAG. Numerical profiles, higher-precision refits, and parameter-recovery experiments show that marginal persistence and copula persistence are only weakly separated in this short discrete series. The results therefore support interval integration as the correct observation layer while showing that conclusions about latent dynamic dependence must be conditioned on the specification of the count margin.

stat.ME↗

arXiv2026

From Common-Slot Chains to Heisenberg Central Products over Global Fields

Let $F$ be a global field and let $p$ be an odd prime with $p\neq\operatorname{char}F$. Assuming first that $μ_p\subset F$, we record in a uniform global-field form the length-four common-slot chain for equal degree-$p$ symbol classes and emphasize the signed normalization adapted to explicit norm constructions. Thus, from \[(a,b)_p=(c,d)_p\in\textrm{Br}(F)[p]\] one obtains $x,y\in F^\times$ such that \[(a,b)_p=(x^{-1},b)_p=(x,y)_p=(c^{-1},y)_p=(c,d)_p.\] For number fields, the underlying chain is the length-four chain lemma of Gille--Szamuely, based on Tate's simultaneous local--global theorem. The point developed here is that its signed form yields four compatible norm equations that can be used constructively. For the extraspecial central product $H_{p^3}*H_{p^3}$ over a $C_p^4$-Kummer extension, the central-embedding obstruction is $(a,b)_p-(c,d)_p$, while the four norm equations supplied by the chain assemble, under a natural independence hypothesis on the auxiliary Kummer classes, into an explicit factorized radical realization of the central product. Finally, when the ground field does not contain $μ_p$, we show by a restriction--corestriction argument that the central-embedding obstruction is detected after passage to the cyclotomic extension $F(μ_p)$. Over that field the problem is Kummer, and the obstruction is again the difference of the two symbol classes.

math.NT↗

arXiv2026

Higher Massey Products in Demuškin Variations: Support Blocks, One-Relator Reduction, and a Five-Fold Vanishing Case

Blumer and Quadrelli introduced a family $\mathcal{F}_2$ of two-relator pro-$p$ groups obtained from a Demuškin group by imposing the commutativity of two generators which are not paired in the Demuškin relation. They proved the triple and quadruple Massey vanishing properties and asked whether the same holds in every length. We introduce the $z$-profile $v_h=(α_h(z_1),α_h(z_2))\in\Fp^2$ of a defined $n$-fold Massey product. Definability forces $\det(v_h,v_{h+1})=0$, so the nonzero profile entries decompose into support blocks carrying projective directions in $\PP^1(\mathbb{F}_p)$. After the known endpoint reduction, profiles with exactly $r$ blocks are counted by $\binom{n-1}{2r}$, and $r$ blocks first occur in length $2r+1$. We also prove an all-length conditional reduction for Dwyer's lifting problem: if the added commuting relator can be made exact in a lift, then the remaining central defect of the Demuškin relator can be removed by an endpoint correction. The correction preserves the power term $x_1^q$ for every parameter allowed in $\mathcal{F}_2$. In length five, this yields vanishing whenever all three interior profile vectors $v_2,v_3,v_4$ are nonzero, for every prime $p$. The resulting classification identifies the remaining five-fold support types and the compatibility mechanisms governing them.

math.GR↗

arXiv2026

Fibre-Product Stability, Kummer Gluing, and Composita for Universal Koszulity

We study universal Koszulity under algebraic gluing and field composita. For quadratic fibre products, orthogonally split pullbacks reduce to direct sums, while Stanley--Reisner pullbacks arise from graph gluing preserving universal Koszulity under a dominating-clique hypothesis. For composita, Kummer theory and the norm-residue theorem yield a graph criterion from restriction images and degree-two cup-product relations, verified for iterated Laurent-series fields with nonzero mixed symbols. In a nonabelian RAAG family, every finite $p$-extension has explicitly determined universally Koszul cohomology, with \[ G_L(p)\cong F_{1+q(d-1)}\times\mathbb Z_p^s.\]

math.NT↗

arXiv2026

Coordinate-Deletion Bundles from Composition Algebras: Hopf Defects, $KO$-Classes, and Real Projective Space

Let $D\in\{\C,\Hh,\Oct\}$ be a real composition division algebra of dimension $d\in\{2,4,8\}$. We construct an explicit rank-$d$ real vector bundle $ E_D\longrightarrow\RP^d$ by deleting one homogeneous coordinate on each standard affine chart, interpreting the remaining coordinates as an element of $D$, and using the corresponding left-multiplication matrices as transition data. The bundle admits a matrix-determined trivialization away from the $d+1$ coordinate points. Relative to this trivialization, each deleted point has local clutching map $S^{d-1}\longrightarrow\SO(d),\; u\longmapsto L_u$, which is respectively the complex, quaternionic, or octonionic Hopf clutching map. A section arising from the same matrices has exactly the coordinate points as nondegenerate zeros. Consequently, $w(E_D)=1+x^d$, and real $K$-theory together with Euler-class cancellation gives $E_D\congγ^{\oplus d}$. Thus the construction supplies explicit framed-defect realizations of these familiar bundles. In particular, it gives a semialgebraic octonionic realization of $γ^{\oplus8}$ on $\RP^8$ with nine specified local Hopf defects. We also describe the associated Pfister quadratic bundle over arbitrary fields.

math.AT↗

arXiv2026

Asymptotic Universal Koszulity in Galois Cohomology

We introduce the notion of asymptotic universal Koszulity for graded-commutative algebras generated in degree~$1$, capturing the idea that an infinite-dimensional algebra can be approximated by a filtered system of finite-type universally Koszul quadratic subalgebras. We establish basic structural properties of this class, including stability under filtered colimits, direct products, and base change, as well as a local finite-type criterion expressed in terms of finite-dimensional subspaces of the degree-one component. In the context of Galois cohomology, we prove a colimit theorem for pro-$p$ groups under mild assumptions, showing that cohomology rings arise as filtered colimits of finite quotients. This yields a general criterion under which the cohomology algebra of a profinite group is asymptotically universally Koszul. We further analyze finitely generated quotients via a finite-type capture result, identifying their cohomology with canonical quadratic subalgebras of the ambient algebra. Finally, we formulate conditional local--global and patching principles that isolate the mechanisms by which asymptotic universal Koszulity may arise in arithmetic settings. These results provide a flexible structural framework linking homological algebra, quadratic algebras, and Galois cohomology, and suggest several directions for further investigation.

math.NT↗

arXiv2026

Ramification Subgroups of Knot Groups and their Profinite and Cohomological Structure

We formalize a ramification theory for finite covers of knot exteriors. Given a knot group $G_K$ and a finite-index subgroup $U\le G_K$, we define meridional inertia subgroups $U\cap g\langle m\rangle g^{-1}$ and the global ramification subgroup $M_U\triangleleft U$ as their normal closure. We then analyze $M_U$ from three complementary viewpoints: (1) finite quotients, where $U/M_U$ is shown to be the universal ``maximal meridionally unramified'' quotient of $U$; (2) profinite completions, where we identify the closed ramification subgroup $\widehat M_{\widehat U}$ as the closed normal subgroup generated by closed inertia and prove that meridian-preserving isomorphisms of profinite completions preserve inertia and ramification; (3) cohomology, where ``unramified'' $H^1$-classes (discrete and profinite) are characterized as those vanishing on all inertia subgroups, in direct analogy with number-theoretic inertia conditions in Galois cohomology.

math.GT↗

arXiv2026

Local Nonconvexity Indices for $C^{1,1}$ Functions via Generalized Hessians

Davydov, Moldavskaya, and Zitikis introduced local indices for quantifying the lack of convexity of a $C^2$ function by measuring the nuclear-norm distance of its Hessian from the cone of positive semidefinite matrices. This paper develops a local analogue for functions of class $C^{1,1}$. At a point $x$, the classical Hessian is replaced by the Clarke-type generalized Hessian set $\Hess(h;x)$, defined as the closed convex hull of limiting Hessians at nearby twice differentiability points. Evaluating the same spectral functional over $\Hess(h;x)$ gives an interval-valued local nonconvexity index whose lower and upper endpoints represent, respectively, the least and greatest visible second-order nonconvexity at $x$. The construction reduces to the original smooth index when $h\in C^2$, vanishes for convex $C^{1,1}$ functions, is invariant under orthogonal changes of variables, satisfies a subadditivity inequality for the upper endpoint under sums, and is upper semicontinuous in its upper endpoint. We also relate the upper endpoint to a pointwise weak-convexity curvature modulus and give explicit $C^{1,1}\setminus C^2$ examples. The paper is deliberately local in scope: it proposes a scalar diagnostic extracted from generalized Hessian sets, not a replacement for the richer second-order variational theory of nonsmooth convexity.

math.OC↗

arXiv2020

Enhanced Koszul properties in Galois cohomology

We prove that Galois cohomology satisfies several surprisingly strong versions of Koszul properties, under a well known conjecture, in the finitely generated case. In fact, these versions of Koszulity hold for all finitely generated maximal pro-$p$ quotients of absolute Galois groups which are currently understood. We point out several of these unconditional results which follow from our work. We show how these enhanced versions are preserved under certain natural operations on algebras, generalising several results that were previously established only in the commutative case.

math.RA↗