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The balanced tensor product M (x)_A N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M x N. The balanced tensor product M [x]_C N of two module categories over a monoidal linear category C is the linear category corepresenting C-balanced right-exact bilinear functors out of the product category M x N. We show that the balanced tensor product can be realized as a category of bimodule objects in C, provided the monoidal linear category is finite and rigid., Comment: 19 pages; v3 is author-final version

Conformal nets provide a mathematical model for conformal field theory. We define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. We introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect, provided the fusion occurs over a conformal net of finite index. There is a notion of sector (or bimodule) between two defects, and operations of horizontal and vertical fusion of such sectors. Our most difficult technical result is that the horizontal fusion of the vacuum sectors of two defects is isomorphic to the vacuum sector of the fused defect. Equipped with this isomorphism, we construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions and the vertical fusion of two horizontal fusions of sectors.

We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.

Pontine and forebrain cholinergic nuclei contribute to the regulation of breathing and arousal. This report summarizes experiments in rat ( n = 20) concerning the cholinergic interaction between pons and basal forebrain. In vitro [ 35 S]guanylyl-5′-O-(γ-thio)-triphosphate ([ 35 S]GTPγS) autoradiography quantified carbachol-stimulated guanine nucleotide binding (G) protein activation in seven basal forebrain nuclei. Carbachol significantly increased [ 35 S]GTPγS binding in the vertical and horizontal limbs of the diagonal band of Broca, medial and lateral septum, and nucleus basalis (B)/substantia innominata (SI). In vitro receptor autoradiography demonstrated muscarinic receptors in the same nuclei where carbachol caused G protein activation. In vivo experiments showed that carbachol administered to the pontine reticular formation (PnO) significantly decreased the number of 7–14 Hz spindles in the electroencephalogram (EEG), decreased acetylcholine release in SI, and decreased respiratory rate. Carbachol microinjection into SI did not alter the number of EEG spindles or respiratory rate. The results help clarify that EEG and rate of breathing are more effectively modulated by cholinergic neurotransmission in PnO than in SI.

STUDY OBJECTIVES The cholinergic model of rapid eye movement (REM) sleep has contributed significantly to understanding sleep neurobiology and sleep-dependent respiratory depression. The model has been used extensively in cat and rat, but no previous studies have demonstrated cholinergic REM sleep enhancement in mouse. The present study used microinjection of neostigmine into pontine reticular formation of mouse to test the hypothesis that enhancing pontine cholinergic neurotransmission would cause increased REM sleep and sleep disordered breathing. DESIGN Mice (n=8) were anesthetized and implanted with electrodes for measuring cortical electroencephalogram (EEG). Stainless steel cannulae were stereotaxically implanted to permit subsequent microinjections of 50 nl neostigmine (0.133 microg; 8.8 mM) or saline into the pontine reticular formation. Following recovery, an intensive within-subjects design was used to obtain measures of sleep/wake states, breathing, and locomotor activity. Inferential statistics were provided by t-tests. A probability value of < 0.05 indicated statistical significance. SETTING NA. PATIENTS OR PARTICIPANTS NA. INTERVENTIONS NA. MEASUREMENTS AND RESULTS Behavioral observations and manual scoring of polygraphic recordings showed that neostigmine produced a REM sleep-like state. EEG power analysis using Fast Fourier Transformation confirmed that pontine neostigmine caused EEG activation. Plethysmography demonstrated significantly disordered breathing. Compared to waking, pontine microinjection of neostigmine decreased respiratory rate (-64%) and minute ventilation (-75%). Pontine neostigmine significantly increased duration of inspiration (138%) and expiration (140%) above waking levels and decreased inspiratory flow (-69%). Additional studies showed that pontine neostigmine significantly depressed locomotor activity. CONCLUSIONS This study is the first to demonstrate cholinergic REM sleep enhancement in unanesthetized, intact mouse. The results encourage future studies to characterize similarities and differences in cholinergic REM sleep enhancement in additional inbred strains and in transgenic mice. Such comparisons will help characterize sleep and breathing as intermediate phenotypes that are determined, in part, by the lower level phenotype of pontine cholinergic neurotransmission.

We describe a coordinate-free perspective on conformal nets, as functors from intervals to von Neumann algebras. We discuss an operation of fusion of intervals and observe that a conformal net takes a fused interval to the fiber product of von Neumann algebras. Though coordinate-free nets do not a priori have vacuum sectors, we show that there is a vacuum sector canonically associated to any circle equipped with a conformal structure. This is the first in a series of papers constructing a 3-category of conformal nets, defects, sectors, and intertwiners., Updated to published version

We present a framework for the analysis and synthesis of acoustical instruments based on data-driven probabilistic inference modeling. Audio time series and boundary conditions of a played instrument are recorded and the non-linear mapping from the control data into the audio space is inferred using the general inference framework of Cluster-Weighted Modeling. The resulting model is used for real-time synthesis of audio sequences from new input data.

Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary an algebra-module over this 2-algebra, such that a natural gluing property is satisfied. Moreover, with a view toward the structure of a potential Floer homology theory of 3-manifolds with codimension-two corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing., Comment: a few minor revisions

We observe that the Poincaré duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq1, Sq2, and Sq4 on the cohomology of a string manifold has a symmetry around the middle dimension. We characterize this kind of cohomology operation duality in terms of the annihilator of the Thom class of the negative tangent bundle, and in terms of the vanishing of top-degree cohomology operations. We also indicate how the existence of such an operation-preserving duality implies the integrality of certain polynomials in the Pontryagin classes of the manifold.

Introduction Assessment of cardiovascular parameters, including the electrocardiogram (ECG) is required by the regulatory guidelines. In safety pharmacology studies, this is typically done using chronically implanted radiotelemetry devices in non-rodent species. Methods We compared ECG signal quality from ten male beagle dogs and 10 male cynomolgus monkeys with telemetry transmitters implanted using two surgical approaches: i) epicardial ECG lead placement via single incision, left side thoracotomy or ii) subcutaneous ECG lead placement via laparotomy. In addition, epicardial leads and semi-automated scoring were used in combination to detect changes in ECG values caused by moxifloxacin. Telemetry-instrumented male beagle dogs (n = 8) and male cynomolgus monkeys (n = 8) were given moxifloxacin at 10, 30, or 100 mg/kg (dogs) and 10, 50, or 175 mg/kg (monkeys) as a single dose by oral gavage. Results ECG signals were of excellent quality with epicardial lead placement, and human activity in the room did not significantly alter signal quality. Administration of moxifloxacin was associated with prolongation of QTc interval, in both dogs and monkeys in a dose-dependant pattern. Dogs given 30 mg/kg and 100 mg/kg, the maximum QTcf interval prolongations were 22 ms (+ 9%, 8 h postdose) and 60 ms (+ 24%, 15 h postdose). In monkeys given 50 and 175 mg/kg, the QTcb interval was significantly prolonged from 1 to 6 h postdose, and QTcb interval prolongation persisted in monkeys given 175 mg/kg through 19 h postdose. In monkeys given 175 mg/kg, the maximum QTcb interval prolongation was 43 ms (+ 12.9%, 16 h postdose). Discussion The present study demonstrated that placing leads directly on the epicardium drastically diminishes signal disruption due to room disturbances and subsequent animal excitement. This novel surgical model demonstrated adequate sensitivity to detect changes in ECG parameters, specifically QTc interval prolongation in both the dog and monkey.

We prove that there is a finite level-independent bound on the number of relations defining the fusion ring of positive energy representations of the loop group of a simple, simply connected Lie group. As an illustration, we compute the fusion ring of G 2 at all levels.

Neuronal firing patterns, neuromodulators, and cerebral metabolism change across sleep–waking states, and the synaptic release of glutamate is critically involved in these processes. Extrasynaptic glutamate can also affect neural function and may be neurotoxic, but whether and how extracellular glutamate is regulated across sleep–waking states is unclear. To assess the effect of behavioral state on extracellular glutamate at high temporal resolution, we recorded glutamate concentration in prefrontal and motor cortex using fixed-potential amperometry in freely behaving rats. Simultaneously, we recorded local field potentials (LFPs) and electroencephalograms (EEGs) from contralateral cortex. We observed dynamic, progressive changes in the concentration of glutamate that switched direction as a function of behavioral state. Specifically, the concentration of glutamate increased progressively during waking (0.329 ± 0.06%/min) and rapid eye movement (REM) sleep (0.349 ± 0.13%/min). This increase was opposed by a progressive decrease during non-REM (NREM) sleep (0.338 ± 0.06%/min). During a 3 h sleep deprivation period, glutamate concentrations initially exhibited the progressive rise observed during spontaneous waking. As sleep pressure increased, glutamate concentrations ceased to increase and began decreasing despite continuous waking. During NREM sleep, the rate of decrease in glutamate was positively correlated with sleep intensity, as indexed by LFP slow-wave activity. The rate of decrease doubled during recovery sleep after sleep deprivation. Thus, the progressive increase in cortical extrasynaptic glutamate during EEG-activated states is counteracted by a decrease during NREM sleep that is modulated by sleep pressure. These results provide evidence for a long-term homeostasis of extracellular glutamate across sleep–waking states.

We investigate higher topological cyclic homology as an approach to studying chromatic phenomena in homotopy theory. Higher topological cyclic homology is constructed from the fixed points of a version of topological Hochschild homology based on the n-dimensional torus, and we propose it as a computationally tractable cousin of n-fold iterated algebraic K-theory. The fixed points of toral topological Hochschild homology are related to one another by restriction and Frobenius operators. We introduce two additional families of operators on fixed points, the Verschiebung, indexed on self-isogenies of the n-torus, and the differentials, indexed on n-vectors. We give a detailed analysis of the relations among the restriction, Frobenius, Verschiebung, and differentials, producing a higher analog of the structure Hesselholt and Madsen described for 1-dimensional topological cyclic homology. We calculate two important pieces of higher topological cyclic homology, namely topological restriction homology and topological Frobenius homology, for the sphere spectrum. The latter computation allows us to establish the Segal conjecture for the torus, which is to say to completely compute the cohomotopy type of the classifying space of the torus.

Respiratory and arousal state control are heritable traits in mice. B6.V-Lepob (ob) mice are leptin deficient and differ from C57BL/6J (B6) mice by a variation in the gene coding for leptin. The ob mouse has morbid obesity and disordered breathing that is homologous to breathing of obese humans. This study tested the hypothesis that microinjecting neostigmine into the pontine reticular nucleus, oral part (PnO), of B6 and ob mice alters sleep and breathing. In B6 and ob mice, neostigmine caused a concentration-dependent increase ( P < 0.0001) in percentage of time spent in a rapid eye movement (REM) sleeplike state (REM-Neo). Relative to saline (control), higher concentrations of neostigmine increased REM-Neo duration and the number of REM-Neo episodes in B6 and ob mice and decreased percent wake, percent non-REM, and latency to onset of REM-Neo ( P < 0.001). In B6 and ob mice, REM sleep enhancement by neostigmine was blocked by atropine. Differences in control amounts of sleep and wakefulness between B6 and the congenic ob mice also were identified. After PnO injection of saline, ob mice spent significantly ( P < 0.05) more time awake and less time in non-REM sleep. B6 mice displayed more ( P < 0.01) baseline locomotor activity than ob mice, and PnO neostigmine decreased locomotion ( P < 0.0001) in B6 and ob mice. Whole body plethysmography showed that PnO neostigmine depressed breathing ( P < 0.001) in B6 and ob mice and caused greater respiratory depression in B6 than ob mice ( P < 0.05). Western blot analysis identified greater ( P < 0.05) expression of M2 muscarinic receptor protein in ob than B6 mice for cortex, midbrain, cerebellum, and pons, but not medulla. Considered together, these data provide the first evidence that pontine cholinergic control of sleep and breathing varies between mice known to differ by a spontaneous mutation in the gene coding for leptin.

We prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n-1 generators tensor a cyclic group. We give a detailed description of the order of this cyclic group in terms of the dimensions of irreducible representations of G and show that the congruences determining this cyclic order lift along the twisted index map to relations in the twisted Spin-c bordism group of G., Comment: 38 pages, 2 figures. Added table of contents, remarks in sections 1.2 and 4.1.2

Recent pharmacological studies exploring the functional roles of muscarinic cholinergic receptor (mAChR) subtypes in prefrontal cortex of C57BL/6J (B6) mouse have provided evidence for a presynaptic M2 autoreceptor. The B6 mouse was chosen for these studies because it is a genetically well-characterized model that also provides the genomic background for many genetically modified mice. In addition to increasing ACh release, one functional consequence of pharmacologically blocking the cortical M2 autoreceptor is activation of the contralateral prefrontal cortical EEG. To date, the mechanisms through which M2 autoreceptor antagonism causes cortical EEG activation have not been investigated. The present study tested the hypothesis that, in the B6 mouse, prefrontal cortical ACh activates the contralateral prefrontal EEG via postsynaptic M1 receptors. This hypothesis was tested in 15 mice using in vivo microdialysis delivery of muscarinic antagonists with simultaneous quantification of ACh release, number of 7- to 14-Hz EEG spindles, and fast Fourier transformation analysis of prefrontal EEG. Dialysis delivery of the nonsubtype selective muscarinic antagonist scopolamine (10 nM) significantly ( P = 0.01) increased ACh release. Quantitative EEG analysis showed that scopolamine did not alter contralateral prefrontal cortical EEG. To differentiate mAChR subtypes mediating pre- versus postsynaptic responses, additional experiments used muscarinic antagonists with different affinities for the five mAChR subtypes. Microdialysis delivery of 3 nM AF-DX 116, a muscarinic antagonist with relatively high affinity for the M2 and M4 subtypes, significantly ( P < 0.01) increased prefrontal cortical ACh release and activated EEG in the contralateral prefrontal cortex. EEG activation was characterized by a significant decrease in number of 7- to 14-Hz EEG spindles ( P < 0.0001) and power ( Vrms) of EEG slow waves ( P < 0.05). Microdialysis delivery of 3 nM AF-DX 116 plus 3 nM pirenzepine, a relatively selective M1 and M4 muscarinic antagonist, also significantly ( P < 0.01) increased ACh release but did not decrease the number of EEG spindles and did not change EEG slow waves. The differential EEG and ACh responses to dialysis delivery of the muscarinic antagonists support the conclusion that, in B6 mouse, postsynaptic muscarinic receptors of the M1 subtype are a primary site by which ACh activates the EEG.

Comprehensive digital analysis and synthesis of musical instruments using direct observations of their physical behavior have been developed and implemented for the violin. In a training session, control input data from unobtrusive bow and finger sensors is recorded simultaneously with the violin’s audio output. These signals are used to train a cluster‐weighted probabilistic prediction model that reproduces the nonlinear relationship between the control inputs and the target audio output data. Cluster‐weighted modeling was developed to apply previous results from linear systems theory and time‐series approximation theory in the broader context of a globally complex and nonlinear model. The presented sound synthesis engine makes use of familiar sound synthesis techniques, but extends them with a complex input/output framework that naturally incorporates dynamic control. The final system predicts audio data based on new control data. While a violinist plays the interface device (a silent violin), the computer model reproduces the sound of the original violin. Recent work has extended the system of sensors and algorithms to model string vibration dynamics as well as the radiated sound.

Recent evidence suggests that muscarinic cholinergic receptors of the M2 subtype serve as autoreceptors modulating acetylcholine (ACh) release in prefrontal cortex. The potential contribution of M2 autoreceptors to excitability control of prefrontal cortex has not been investigated. The present study tested the hypothesis that M2 autoreceptors contribute to activation of the cortical electroencephalogram (EEG) in C57BL/6J (B6) mouse. This hypothesis was evaluated using microdialysis delivery of the muscarinic antagonist AF-DX116 (3 nM) while simultaneously quantifying ACh release in prefrontal cortex, number of 7- to 14-Hz EEG spindles, and EEG power spectral density. Mean ACh release in prefrontal cortex was significantly increased ( P < 0.0002) by AF-DX116. The number of 7- to 14-Hz EEG spindles caused by halothane anesthesia was significantly decreased ( P < 0.0001) by dialysis delivery of AF-DX116 to prefrontal cortex. The cholinergically induced cortical activation was characterized by a significant ( P < 0.05) decrease in slow-wave EEG power. Together, these neurochemical and EEG data support the conclusion that M2 autoreceptor enhancement of ACh release in prefrontal cortex activates EEG in contralateral prefrontal cortex of B6 mouse. EEG slow-wave activity varies across mouse strains, and the results encourage comparative phenotyping of cortical ACh release and EEG in additional mouse models.

Background Shaker codes for a Drosophila voltage-dependent potassium channel. Flies carrying Shaker null or hypomorphic mutations sleep 3–4 h/day instead of 8–14 h/day as their wild-type siblings do. Shaker-like channels are conserved across species but it is unknown whether they affect sleep in mammals. To address this issue, we studied sleep in Kcna2 knockout (KO) mice. Kcna2 codes for Kv1.2, the alpha subunit of a Shaker-like voltage-dependent potassium channel with high expression in the mammalian thalamocortical system. Results Continuous (24 h) electroencephalograph (EEG), electromyogram (EMG), and video recordings were used to measure sleep and waking in Kcna2 KO, heterozygous (HZ) and wild-type (WT) pups (P17) and HZ and WT adult mice (P67). Sleep stages were scored visually based on 4-s epochs. EEG power spectra (0–20 Hz) were calculated on consecutive 4-s epochs. KO pups die by P28 due to generalized seizures. At P17 seizures are either absent or very rare in KO pups (< 1% of the 24-h recording time), and abnormal EEG activity is only present during the seizure. KO pups have significantly less non-rapid eye movement (NREM) sleep (-23%) and significantly more waking (+21%) than HZ and WT siblings with no change in rapid eye movement (REM) sleep time. The decrease in NREM sleep is due to an increase in the number of waking episodes, with no change in number or duration of sleep episodes. Sleep patterns, daily amounts of sleep and waking, and the response to 6 h sleep deprivation are similar in HZ and WT adult mice. Conclusion Kv1.2, a mammalian homologue of Shaker, regulates neuronal excitability and affects NREM sleep.