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Masaki Izumi

Publications and source records attributed to Masaki Izumi.

At least 19 recordsLinked to original sources

PHASE: A Physiology-Guided Hierarchical Foundation Model for Intracranial EEG

Clinicians and neuroscientists have long analyzed intracranial electroencephalography (iEEG) through directly measurable physiological characteristics, which carry much of the information that downstream tasks depend on. Recent iEEG foundation models learn by reconstructing or predicting their inputs, which leaves the retention of these characteristics implicit. They are also evaluated mainly on cognitive decoding and a narrow clinical task, i.e., seizure detection. On a broad, clinically relevant benchmark such as Omni-iEEG, they remain below task-specific models when used frozen. We introduce PHASE, a physiology-guided foundation model that makes these characteristics explicit learning targets, pairing them with masked latent prediction in a temporal stage (PHASE-T) within each channel and a spatiotemporal stage (PHASE-ST) across synchronized channels. PHASE is pretrained on heterogeneous recordings from 222 participants at nine clinical sites. On all five Omni-iEEG clinical tasks, frozen PHASE-T outperforms every evaluated foundation model by up to 31\%, and fine-tuned PHASE-T surpasses the task-specific models, setting a new state of the art. PHASE-T benefits from physiological supervision, outperforming variants trained with latent prediction alone or auxiliary waveform reconstruction on every task in matched ablations. PHASE-T generalizes to unseen institutions, outperforming the compared models with few or no local labels. PHASE-ST further improves seizure-onset-zone identification over PHASE-T and, when frozen, decodes sound volume and pitch on BrainTreebank better than published models. Beyond task performance, PHASE learns to encapsulate the physiological characteristics clinicians recognize, from seizure onset and its propagation to anatomical region identity, even though its pretraining contains no ictal recordings or anatomical labels.

cs.LG↗

Toward the classification of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups

Strongly self-absorbing $\mathrm{C}^*$-algebras play a distinguished role in the classification of nuclear $\mathrm{C}^*$-algebras. Their dynamical analogues were introduced and extensively studied by Szabó. In this paper, we propose a conjecture regarding the equivariant $KK$-theory of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups in the equivariant bootstrap category; an affirmative answer to this conjecture would lead to classification results. We settle this conjecture for all finite EPPO (every element has a prime-power order) groups. In the course of our proof, we establish a Künneth-type formula for the equivariant $K$-theory of $\mathrm{C}^*$-algebras equipped with finite cyclic group actions -- more precisely, for the cyclotomic part of the equivariant $K$-groups introduced by Meyer and Nadareishvili -- under a certain unique divisibility assumption.

math.OA↗

A family of matrix flows converging to normal matrices

The celebrated Antezana-Pujals-Stojanoff Theorem states that the iterated Aluthge transforms of an arbitrary matrix converge to a normal matrix. We introduce a family of matrix flows that share this convergence property by defining them through ordinary differential equations. The family includes a continuous analogue of the Aluthge transform, as well as a differential equation discussed by Haagerup in the context of II$_1$ factors. We also examine the same type of flows in the setting of Hilbert space operators equipped with unitarily invariant norms.

math.FA↗

G-kernels and Crossed Modules

We develop a unified framework based on topological crossed modules for various lifting obstructions for $Γ$-kernels. It allows us to identify actions, cocycle actions and $Γ$-kernels up to their natural equivalence relations with cohomology sets. The obstructions then appear as boundary maps in corresponding exact sequences. Since topological crossed modules are topological $2$-groups (in the categorical sense), they have classifying spaces, which come with a natural transformation from the cohomology to a homotopy set. For the crossed module that gives cocycle actions we prove a weak equivalence of the classifying space of the crossed module with one from bundle theory. In case the algebra is strongly self-absorbing we show that the homotopy set is a group and that the above natural transformation is a group isomorphism on an appropriate restriction of the cohomology set.

math.OA↗

Determination of the distance from a projection to nilpotents

In this note, we study the distance from an arbitrary nonzero projection $P$ to the set of nilpotents in a factor $\mathcal{M}$ equipped with a normal faithful tracial state $τ$. We prove that the distance equals $(2\cos \frac{τ(P)π}{1+2τ(P)})^{-1}$. This is new even in the case where $\mathcal{M}$ is the matrix algebra. The special case settles a conjecture posed by Z. Cramer.

math.OA↗

Minimal compact group actions on C$^*$-algebras with simple fixed point algebras

The notion of qausi-product actions of a compact group on a C$^*$-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm's characterization of non-type I C$^*$-algebras. We show that a faithful minimal action of a second countable compact group on a separable C$^*$-algebra is quasi-product whenever its fixed point algebra is simple. This was previously known only for compact abelian groups and for profinite groups. Our proof relies on a subfactor technique applied to finite index inclusions of simple C$^*$-algebras in the purely infinite case, and also uses ergodic actions of compact groups in the general case. As an application, we show that if moreover the fixed point algebra is a Kirchberg algebra, such an action is always isometrically shift-absorbing, and hence is classifiable by the equivariant KK-theory due to a recent result of Gabe-Szabó.

math.OA↗

$G$-kernels of Kirchberg algebras

A $G$-kernel is a group homomorphism from a group $G$ to the outer automorphism group of a C$^*$-algebra. Inspired by recent work of Evington and Girón Pacheco in the stably finite case, we introduce a new invariant of a $G$-kernel using $K$-theory, and deduce several new constraints of the obstruction classes of $G$-kernels in the purely infinite case. We classify $\mathbb{Z}^n$-kernels for strongly self-absorbing Kirchberg algebras in the bootstrap category in terms of our new invariant and the Dadarlat-Pennig theory of continuous fields of strongly self-absorbing C$^*$-algebras.

math.OA↗

Group-subgroup subfactors revisited

For all Frobenius groups and a large class of finite multiply transitive permutation groups, we show that the corresponding group-subgroup subfactors are completely characterized by their principal graphs. The class includes all the sharply $k$-transitive permutation groups for $k=2,3,4$, and in particular the Mathieu group $M_{11}$ of degree 11.

math.OA↗

Quasicentral modulus and self-similar sets: a supplementary result to Voiculescu's work

In his recent work, Voiculescu generalized his remarkable formula for the quasicentral modulus of a commuting $n$-tuple of hermitian operators with respect to the $(n,1)$-Lorentz ideal to the case where its spectrum is contained in a Cantor-like self-similar set in a certain class. In this note, we treat general self-similar sets satisfying the open set condition, and obtain lower and upper bounds of the quasicentral modulus. Our proof shows that Voiculescu's formula holds for a class of self-similar sets including the Sierpinski gasket and the Sierpinski carpet.

math.FA↗

Graded extensions of generalized Haagerup categories

We classify certain $\mathbb{Z}_2 $-graded extensions of generalized Haagerup categories in terms of numerical invariants satisfying polynomial equations. In particular, we construct a number of new examples of fusion categories, including: $\mathbb{Z}_2 $-graded extensions of $\mathbb{Z}_{2n} $ generalized Haagerup categories for all $n \leq 5 $; $\mathbb{Z}_2 \times \mathbb{Z}_2 $-graded extensions of the Asaeda-Haagerup categories; and extensions of the $\mathbb{Z}_2 \times \mathbb{Z}_2 $ generalized Haagerup category by its outer automorphism group $A_4 $. The construction uses endomorphism categories of operator algebras, and in particular, free products of Cuntz algebras with free group C$^*$-algebras.

math.OA↗

Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories

A unitary fusion category is called $\mathbb{Z}/2\mathbb{Z}$-quadratic if it has a $\mathbb{Z}/2\mathbb{Z}$ group of invertible objects and one other orbit of simple objects under the action of this group. We give a complete classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories. The main tools for this classification are skein theory, a generalization of Ostrik's results on formal codegrees to analyze the induction of the group elements to the center, and a computation similar to Larson's rank-finiteness bound for $\mathbb{Z}/3\mathbb{Z}$-near group pseudounitary fusion categories. This last computation is contained in an appendix coauthored with attendees from the 2014 AMS MRC on Mathematics of Quantum Phases of Matter and Quantum Information.

math.QA↗

Poly-$\mathbb{Z}$ group actions on Kirchberg algebras II

This is the second part of our serial work on the classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of continuous fields of Kirchberg algebras over the classifying spaces. As an application, we determine the number of cocycle conjugacy classes of outer $\mathbb{Z}^n$-actions on the Cuntz algebras.

math.OA↗

Infinite families of potential modular data related to quadratic categories

We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with some conditions on the fixed points of the involutions and the relative sizes of the groups. From this input we construct $S$ and $T$ matrices which satisfy the modular relations and whose Verlinde coefficients are non-negative integers. We also check certain restrictions coming from Frobenius-Schur indicators. These families generalize Evans and Gannon's conjectures for the modular data associated to generalized Haagerup and near-group categories for odd groups, and include the modular data of the Drinfeld centers of almost all known quadratic categories. In addition to the subfamilies which are conjecturally realized by centers of quadratic categories, these families include many examples of potential modular data which do not correspond to known types of modular tensor categories.

math.OA↗

Algebraic realization of noncommutative near-group fusion categories

Noncommutative near-group fusion categories were completely classified in the previous work of the first named author by using an operator algebraic method (and hence under the assumption of unitarity), and they were shown to be group theoretical though the corresponding pointed categories were not identified. In this note we give a purely algebraic construction of the noncommutative near-group fusion categories starting from pointed categories categorically Morita equivalent to them.

math.CT↗

Poly-$\mathbb{Z}$ group actions on Kirchberg algebras I

Toward the complete classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras, we prove several fundamental theorems that are used in the classification. In addition, as an application of them, we classify outer actions of poly-$\mathbb{Z}$ groups of Hirsch length not greater than three on unital Kirchberg algebras up to $KK$-trivial cocycle conjugacy.

math.OA↗

Drinfeld centers of fusion categories arising from generalized Haagerup subfactors

We consider generalized Haagerup categories such that $1 \oplus X$ admits a $Q$-system for every non-invertible simple object $X$. We show that in such a category, the group of order two invertible objects has size at most four. We describe the simple objects of the Drinfeld center and give partial formulas for the modular data. We compute the remaining corner of the modular data for several examples and make conjectures about the general case. We also consider several types of equivariantizations and de-equivariantizations of generalized Haagerup categories and describe their Drinfeld centers. In particular, we compute the modular data for the Drinfeld centers of a number of examples of fusion categories arising in the classification of small-index subfactors: the Asaeda-Haagerup subfactor; the $3^{\Z_4} $ and $3^{\Z_2 \times \Z_2} $ subfactors; the $2D2$ subfactor; and the $4442$ subfactor. The results suggest the possibility of several new infinite families of quadratic categories. A description and generalization of the modular data associated to these families in terms of pairs of metric groups is taken up in the accompanying paper \cite{GI19_2}.

math.OA↗

The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra $O_{n+1}$ for finite n in terms of K-theory. We show that there is an example of a space for which the homotopy set is a non-commutative group, and hence the classifying space of the automorphism group of the Cuntz algebra for finite n is not an H-space. We also make an improvement of Dadarlat's classification of continuous fields of the Cuntz algebras in terms of vector bundles.

math.OA↗