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We obtain a weak homotopy equivalence type result between two topological groups associated with a Kirchberg algebra: the unitary group of the continuous asymptotic centralizer and the loop group of the automorphism group of the stabilization. This result plays a crucial role in our subsequent work on the classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras. As a special case, we show that the $K$-groups of the continuous asymptotic centralizer are isomorphic to the $KK$-groups of the Kirchberg algebra., 32 pages

The globus pallidus internus(GPi)has evolved as a potential target for deep brain stimulation(DBS)in patients with advanced Parkinson's disease(PD). GPi stimulation has a significant impact on intractable hyperkinetic movement disorders. Optimal surgical procedures require a combination of image-based targeting and intraoperative microelectrode recording(MER)strategies. Provocation with stimulation through microelectrode or a DBS electrode is also crucial for refining the appropriate electrode position and obtaining a wide therapeutic window of stimulation parameters. In patients with PD, the best target for deep brain stimulation, whether subthalamic nucleus(STN)or the GPi, has been a subject of interest in recent medical literature. STN remains the preferred target for DBS in patients with advanced PD worldwide. In postoperative medication reduction, numerous data support that STN stimulation reduces the total dose of anti-parkinsonian drugs compared to GPi stimulation. However, GPi stimulation has shown a direct anti-dyskinetic effect, without reducing levodopa. Thus, GPi stimulation might be recommended for patients with neurocognitive or neuropsychiatric issues. GPi stimulation has a potential for treating hyperkinetic movement disorders. In patients with PD, STN stimulation is preferred worldwide; however, GPi stimulation has a clinical advantage only for select patients.

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.

Background Compression of the trigeminal nerve by vessels and tumors causes trigeminal neuralgia. However, a tethering effect, provoking an abnormal root-stretching force, has been previously reported to play a role in trigeminal nerve hyperexcitability. We report 2 patients with vestibular schwannomas treated by stereotactic radiosurgery (SRS) who presented with typical manifestations of trigeminal neuralgia after tumor shrinkage. Furthermore, we discuss the mechanisms of trigeminal neuralgia. Case Description Two patients without a history of trigeminal dysfunction, including trigeminal neuralgia, underwent SRS for vestibular schwannomas. Both patients demonstrated tumor shrinkage after transient tumor expansion following SRS. Neither patient presented with facial pain or dysesthesia at the time of peak tumor volume. However, trigeminal neuralgia occurred after tumor shrinkage. One patient underwent surgery, as the neuralgia was refractory to medical treatment; although the trigeminal nerve was adhered and tethered to the tumor, no neurovascular conflict was identified between the tumor and the nerve. We removed the tumor partially, dissecting between the nerve and the tumor, and relieved the tethered effect. Trigeminal neuralgia was relieved without medication after surgery. Conclusions The present cases demonstrate a tethered effect of tumor shrinkage after SRS, which was considered to play a role in trigeminal neuralgia. Surgical dissection surrounding the nerve root is effective for medically resistant neuralgia, even if the tumor shrinks. Partial tumor removal is adequate in such cases, as the tumor has been controlled by radiosurgery.

Objective Deep brain stimulation (DBS) of the bilateral subthalamic nucleus (STN) is a standard surgical treatment option in patients with advanced Parkinson's disease. Adverse effects on cognitive function have been reported, impacting the quality of life of patients and caregivers. We aimed to investigate a quantitative predictive preexisting cognitive factor for predicting postoperative cognitive changes. Methods Thirty-five patients underwent STN-DBS. A battery of neuropsychological tests were used to examine executive function, processing speed, and visuospatial function both preoperatively and 1 year postoperatively. A multiple logistic regression analysis was performed to investigate the relationships between preoperative factors and cognitive outcomes. The predictive value of the preoperative factors for global cognitive decline during long-term follow-up were evaluated. Results The patients exhibited significant changes in processing speed and visuospatial function after surgery. Using reliable change index values, lower preoperative scores on the Similarities and Object Assembly subtests of the Wechsler Adult Intelligence Scale III were associated with decreases in visuospatial function at 1 year after DBS. The odds ratios were 10.2 for Similarities and 9.53 for Object Assembly. The proportion of Mini Mental State Examination–maintained patients with low scores on the Similarities subtest was significantly lower than that of patients with high scores at 3 and 5 years. No factors were found to be related to decreases in processing speed. Conclusions Preoperative evaluation of the Similarities and Object Assembly subtests may be useful to identify patients who are at a greater risk of experiencing decreases in visuospatial functioning after STN-DBS. Furthermore, a low score on the Similarities subtest may predict future global cognitive deterioration.

We investigate a (potentially infinite) series of subfactors, called $3^n$ subfactors, including $A_4$, $A_7$, and the Haagerup subfactor as the first three members corresponding to $n=1,2,3$. Generalizing our previous work for odd $n$, we further develop a Cuntz algebra method to construct $3^n$ subfactors and show that the classification of the $3^n$ subfactors and related fusion categories is reduced to explicit polynomial equations under a mild assumption, which automatically holds for odd $n$.In particular, our method with $n=4$ gives a uniform construction of 4 finite depth subfactors, up to dual,without intermediate subfactors of index $3+\sqrt{5}$. It also provides a key step for a new construction of the Asaeda-Haagerup subfactor due to Grossman, Snyder, and the author., Comment: 69 pages. v2: typos in Def. 2.1 and subsection 6.2 corrected

We describe the flows of weights for von Neumann algebras arising from KMS states for the gauge actions of the Cuntz-Pimsner algebras in terms of Poisson (tail) boundaries., Theorem 3.5 corrected for negative $\beta$, and minor corrections done. To appear in Communications in Mathematical Physics

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., Comment: 16 pages

We give an algorithm to compute the $K$-groups of the crossed product by the flip automorphism for a nuclear C$^*$-algebra satisfying the UCT., explanations added. to appear in the proceedings of the 9th MSJ-SI

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., Comment: Corrected typos and other minor editing; mathematica notebook added; appendix merged with main article (the body is the 59 pages)

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., Comment: to appear in Inventiones Mathematicae

We study unitary quotients of the free product unitary pivotal category A2 * T2. We show that such quotients are parametrized by an integer n ≥ 1 and an 2n–th root of unity ω. We show that for n = 1, 2, 3, there is exactly one quotient and ω = 1. For 4 ≤ n ≤ 10, we show that there are no such quotients. Our methods also apply to quotients of T2 * T2, where we have a similar result.The essence of our method is a consistency check on jellyfish relations. While we only treat the specific cases of A2 × T2 and T2 . T2, we anticipate that our technique can be extended to a general method for proving the nonexistence of planar algebras with a specified principal graph.During the preparation of this manuscript, we learnt of Liu's independent result on composites of A3 and A4 subfactor planar algebras (arxiv:1308.5691). In 1994, BischHaagerup showed that the principal graph of a composite of A3 and A4 must fit into a certain family, and Liu has classified all such subfactor planar algebras. We explain the connection between the quotient categories and the corresponding composite subfactor planar algebras. As a corollary of Liu's result, there are no such quotient categories for n ≥ 4.This is an abridged version of arxiv:1308.5723.

The classification of subfactors of small index revealed several new subfactors. The first subfactor above index 4, the Haagerup subfactor, is increasingly well understood and appears to lie in a (discrete) infinite family of subfactors where the ℤ \mathbb{Z} /3 ℤ \mathbb{Z} symmetry is replaced by other finite abelian groups. The goal of this paper is to give a similarly good description of the Asaeda–Haagerup subfactor which emerged from our study of its Brauer–Picard groupoid. More specifically, we construct a new subfactor 𝒮 {\mathcal{S}} which is a ℤ \mathbb{Z} /4 ℤ \mathbb{Z} × \times ℤ \mathbb{Z} /2 ℤ \mathbb{Z} analogue of the Haagerup subfactor and we show that the even parts of the Asaeda–Haagerup subfactor are higher Morita equivalent to an orbifold quotient of 𝒮 {\mathcal{S}} . This gives a new construction of the Asaeda–Haagerup subfactor which is much more symmetric and easier to work with than the original construction. As a consequence, we can settle many open questions about the Asaeda–Haagerup subfactor: calculating its Drinfeld center, classifying all extensions of the Asaeda–Haagerup fusion categories, finding the full higher Morita equivalence class of the Asaeda–Haagerup fusion categories, and finding intermediate subfactor lattices for subfactors coming from the Asaeda–Haagerup categories. The details of the applications will be given in subsequent papers.

We give the classification of subfactor planar algebras at index exactly 5. All the examples arise as standard invariants of subgroup subfactors. Some of the requisite uniqueness results come from work of Izumi in preparation. The non-existence results build upon the classification of subfactor planar algebras with index less than 5, with some additional analysis of special cases., 9 pages

Craniocervical junction arteriovenous fistulas(CCJ-AVFs)are extremely rare lesions that may result in both subarachnoid hemorrhage(SAH)and myelopathy. Diagnosis of CCJ-AVF is difficult and may be delayed due to variable clinical features and a spectrum of neuroradiological findings. To elucidate the clinical characteristics of CCJ-AVF, we analyzed the clinical symptoms, neuroimaging findings, and the results of surgical treatment in five patients.Among the five patients, four were diagnosed with dural AVFs, and the remaining patient was diagnosed with radicular AVF. Two of the five patients presented with SAH, and the rest presented with myelopathy. In both the SAH patients, the initial digital subtraction angiography(DSA)failed to reveal the AVFs, and a definitive diagnosis was made only after repeated DSAs. In two of the three myelopathy patients, the diagnosis was delayed because of nonspecific chronic neurological symptoms which resembled a thoracolumbar lesion. Four patients underwent shunt occlusion through direct surgery and demonstrated favorable outcomes. One myelopathy patient, however, demonstrated abrupt onset, associated with progressive neurological deterioration, which resulted in poor prognosis. The magnetic resonance imaging(MRI)findings, which included intramedullary high intensity on a T2 weighted image, flow void, and varix at the cervical cord, were specific for the myelopathy patients.A thorough 4-vessel DSA study, including the cervical region, is mandatory for SAH patients whose clots are predominantly in the posterior fossa, and repeated DSA must be considered in cases of unknown origin. CCJ-AVF may cause myelopathy, with symptoms such as urinary dysfunction and/or paraparesis. Screening with a cervical MRI is useful for detecting CCJ-AVF in cases of myelopathy. Emergency radical treatment must be attempted for those patients demonstrating abrupt onset associated with symptoms of progressive deterioration, such as respiratory dysfunction or bulbar palsy.

OBJECTIVEEncephalo-myo-synangiosis (EMS) is an effective revascularization procedure for the treatment of moyamoya disease (MMD). However, the temporalis muscle used for EMS sometimes swells and causes ischemic complications by compressing the underlying brain. This study aimed to elucidate the effect of sagittal splitting (SS) of the muscle for prevention of ischemic complications and its impact on the postoperative development of collateral vessels.METHODSIn this historical case-control study, we analyzed 60 hemispheres in adult patients with MMD who underwent EMS using the temporalis muscle from December 1998 to November 2017. The muscle was divided anteroposteriorly by coronal splitting, and the anterior, posterior, or both parts of the muscle were used for EMS in 17, 4, and 39 hemispheres, respectively. In cases performed after 2006, the muscle was halved by SS, and the medial half was used for EMS to reduce the muscle volume (n = 47). The degree of postoperative muscle swelling was evaluated by measuring the maximum thickness of the muscle on CT scans obtained 3 to 7 days after surgery. The collateral developments of the anterior deep temporal artery (aDTA), posterior deep temporal artery (pDTA), and middle temporal artery (MTA) were assessed using digital subtraction angiography and MR angiography performed 6 months or more after surgery.RESULTSSS significantly reduced the temporalis muscle thickness from 12.1 ± 5.0 mm to 7.1 ± 3.0 mm (p < 0.01). Neurological deterioration due to the swollen temporalis muscle developed in 4 of the 13 hemispheres without SS (cerebral infarction in 1, reversible neurological deficit in 2, and convulsion in 1) but in none with SS. There were no significant differences in the postoperative collateral developments of the aDTA, pDTA, and MTA between hemispheres with and without SS. The MTA more frequently developed in hemispheres with EMS in which the posterior part of the muscle was used (30/37) than those in which this part was not used (4/16) (p < 0.01).CONCLUSIONSSS of the temporalis muscle might prevent neurological deterioration caused by the swollen temporalis muscle by reducing its volume without inhibiting the development of the collateral vessels.

We examine what it means to say that certain endomorphisms of a factor (which we call equi-modular) are extendable. We obtain several conditions on an equi-modular endomorphism, and single out one of them with a purely ‘subfactor flavour’ as a theorem. We then exhibit the obvious example of endomorphisms satifying the condition in this theorem. We use our theorem to determine when every endomorphism in an E0-semigroup on a factor is extendable which property is easily seen to be a cocycle-conjugacy invariant of the E0-semigroup. We conclude by giving examples of extendable E0−semigroups, and by showing that the Clifford flow on the hyperfinite II1 factor is not extendable, neither is the free flow. AMS subject classification: Primary 46L55; Secondary 46L40, 46L53, 46C99

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra [Formula: see text] for finite [Formula: see text] in terms of K-theory. We show that there is an example of a space for which the homotopy set is a noncommutative group, and hence, the classifying space of the automorphism group of the Cuntz algebra for finite [Formula: see text] 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.

We show that any faithful quasi-free actions of a finite group on the Cuntz algebra $\mathcal{O}_\infty$ are mutually conjugate, and that they are asymptotically representable.

We classify a large class of Z 2 -actions on the Kirchberg algebras employing the Kasparov group KK 1 as the space of classification invariants.

We consider the harmonic measure on the Gromov boundary of a nonamenable hyperbolic group defined by a finite range random walk on the group, and study the corresponding orbit equivalence relation on the boundary. It is known to be always amenable and of type III. We determine its ratio set by showing that it is generated by certain values of the Martin kernel. In particular, we show that the equivalence relation is never of type III_0., 21 pages

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}., Completely rewritten in 2019, replacing previous version with title "Quantum doubles of generalized Haagerup subfactors and their orbifolds". Includes new results and generalizations of examples from 2015 version. Source includes pdf appendix and mathematica notebook

We classify finite group actions on some classes of C ∗ -algebras with the Rohlin property in terms of the K-groups. A group cohomological obstruction is obtained for the K-groups of a C ∗ -algebra allowing such an action, for example, the Tate cohomology groups with the K-groups as the coefficient modules must vanish. Model actions with the Rohlin property are constructed for given K-theoretical invariants. Quasi-free actions of finite cyclic groups on the Cuntz algebras and their dual actions are investigated from the view point of the Rohlin property.

As an application of the general theory established in the first part, we determine the structure of Longo–Rehren inclusions for several systems of sectors arising from endomorphisms of the Cuntz algebras. The E6 subfactor and the Haagerup subfactor are included among these examples, and the dual principal graphs and the S and T-matrices for their Longo–Rehren inclusions are obtained. We also construct several new subfactors using endomorphisms of the Cuntz algebras, and determine their tube algebra structure.

We investigate the structure of the Longo–Rehren inclusion for a finite closed system of endomorphisms of factors, whose categorical structure is known to be the same as the asymptotic inclusion of A. Ocneanu. In particular, we obtain a precise description of the sectors associated with the Longo–Rehren inclusions in terms of half braidings, which do not necessarily satisfy the usual condition of braidings. In doing so, we give new proofs to most of the known statements concerning asymptotic inclusions. We construct a complete system of matrix units of the tube algebra using the half braidings, which will be used in the second part to describe concrete examples of the Longo–Rehren inclusions arising from the Cuntz algebra endomorphisms. We also discuss the case where the original system has a braiding, and generalize Ocneanu and Evans–Kawahigashi's method for the analysis of the asymptotic inclusions of the Hecke algebra subfactors.

The relationship between index theory and random walks on fusion algebras is discussed. Popa's notion of amenability is reformulated as a property of fusion algebras, and several equivalent conditions of amenability are obtained. A ratio limit theorem is proved as a characterization of amenability. A number of conditions, all equivalent to Popa's notion of strong amenability in the case of subfactors, of a pair of a fusion algebra and a probability measure are proposed, and their relationship is studied from the viewpoint of random walks and entropic densities. Fusion algebra homomorphisms and free products of fusion algebras are also discussed.

The present notes provide a proof of $i^*(\mathbb{C}P+\mathbb{C}(I-P)\,;\mathbb{C}Q+\mathbb{C}(I-Q)) = -\chi_\mathrm{orb}(P,Q)$ for any pair of projections $P,Q$ with $\tau(P)=\tau(Q)=1/2$. The proof includes new extra observations, such as a subordination result in terms of Loewner equations. A study of the general case is also given., Comment: 13 pages

Background To examine the effects of percutaneous endoscopic gastrostomy (PEG) on quality of life (QOL) in patients with dementia. Methods We retrospectively included 53 Japanese community and tertiary hospitals to investigate the relationship between the newly developed PEG and consecutive dementia patients with swallowing difficulty between Jan 1st 2006 and Dec 31st 2008. We set improvements in 1) the level of independent living, 2) pneumonia, 3) peroral intake as outcome measures of QOL and explored the factors associated with these improvements. Results Till October 31st 2010, 1,353 patients with Alzheimer’s dementia (33.1%), vascular dementia (61.7%), dementia with Lewy body disease (2.0%), Pick disease (0.6%) and others were followed-up for a median of 847 days (mean 805 ± 542 days). A total of 509 deaths were observed (mortality 59%) in full-followed patients. After multivariate adjustments, improvement in the level of independent living was observed in milder dementia, or those who can live independently with someone, compared with advanced dementia, characterized by those who need care by someone: Odds Ratio (OR), 3.90, 95% confidence interval (95%CI), 1.59 - 9.39, P = 0.003. Similarly, improvement of peroral intake was noticed in milder dementia: OR, 2.69, 95%CI, 1.17 - 6.17, P = 0.02. Such significant associations were not observed in improvement of pneumonia. Conclusions These results suggest that improvement of QOL after PEG insertion may be expected more in milder dementia than in advanced dementia.

We give a brief account of group actions on operator algebras mainly focusing on classification results. We first recall rather classical results on the classification of discrete amenable group actions on the injective factors, which may serve as potential goals in the case of C∗-algebras for the future. We also mention Galois correspondence type results and quantum group actions for von Neumann algebras. Then we report on the recent developments of the classification of group actions on C∗-algebras in terms of K-theoretical invariants. We give conjectures on the classification of a class of countable amenable group actions on Kirchberg algebras and strongly self-absorbing C∗-algebras, which involve the classifying spaces of the groups. Mathematics Subject Classification (2010). Primary 46L40; Secondary 46L35.

One major obstacle in extending the classification of small index subfactors beyond 3+\sqrt{3} is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the "weeds" Q and Q' from Part 1 (arXiv:1007.1730)). Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed Q' immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds Q and Q'. Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman-de la Harpe-Jones subfactor using a combination of planar algebra techniques and connections., Comment: 21 pages

We show that the number of the conjugacy classes of the AFD type II1 subfactors with the principal graph D1n is n − 2. This gives the last missing number in the complete classfication list of subfactors with index 4 by S. Popa. This also disproves an announcement of A. Ocneanu that such a subfactor is unique for each n. We give two different proofs. One is by an application of an idea of an orbifold model in solvable lattice model theory to Ocneanu′s paragroup theory and the other is by reduction to classification of dihedral group actions. The latter also shows that the AFD type III1 subfactors with the principal graph D1n split as type II1 subfactors tensored with the common AFD type III1 factor. We also discuss a relation between these proofs and a construction of subfactors using Cuntz algebra endomorphisms.