Lifting defects for nonstable K_0-theory of exchange rings and C*-algebras

The assignment (nonstable K_0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: (1) There is no functor F, from simplicial monoids with order-unit with normalized positive homomorphisms to exchange rings, such that VF is equivalent to the identity. (2) There is no functor F, from simplicial monoids with order-unit with normalized positive embeddings to C*-algebras of real rank 0 (resp., von Neumann regular rings), such that VF is equivalent to the identity. (3) There is a {0,1}^3-indexed commutative diagram D of simplicial monoids that can be lifted, with respect to the functor V, by exchange rings and by C*-algebras of real rank 1, but not by semiprimitive exchange rings, thus neither by regular rings nor by C*-algebras of real rank 0. By using categorical tools from an earlier paper (larders, lifters, CLL), we deduce that there exists a unital exchange ring of cardinality aleph three (resp., an aleph three-separable unital C*-algebra of real rank 1) R, with stable rank 1 and index of nilpotence 2, such that V(R) is the positive cone of a dimension group and V(R) is not isomorphic to V(B) for any ring B which is either a C*-algebra of real rank 0 or a regular ring.Comment: 34 pages. Algebras and Representation Theory, to appea

Observer-Based State Feedback for Enhanced Insulin Control of Type ‘I’ Diabetic Patients

During the past few decades, biomedical modeling techniques have been applied to improve performance of a wide variety of medical systems that require monitoring and control. Diabetes is one of the most important medical problems. This paper focuses on designing a state feedback controller with observer to improve the performance of the insulin control for type ‘I’ diabetic patients. The dynamic model of glucose levels in diabetic patients is a nonlinear model. The system is a typical fourth-order single-input-single-output state space model. Using a linear time invariant controller based on an operating condition is a common method to simplify control design. On the other hand, adaptive control can potentially improve system performance. But it increases control complexity and may create further stability issues. This paper investigates patient models and presents a simplified control scheme using observer-based feedback controllers. By comparing different control schemes, it shows that a properly designed state feedback controller with observer can eliminate the adaptation strategy that the Proportional-Integral-Derivative (PID) controllers need to improve the control performance. Control strategies are simulated and their performance is evaluated in MATLAB and Simulink

The homotopy type of the loops on (n−1)(n-1)-connected (2n+1)(2n+1)-manifolds

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by the rank of the free Abelian part of the homology. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.Comment: Trends in Algebraic Topology and Related Topics, Trends Math., Birkhauser/Springer, 2018. arXiv admin note: text overlap with arXiv:1510.0519

Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model

In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED anomaly. In the Sakai-Sugimoto model, which in a certain limit is dual to large-N_c QCD, we discuss the proper implementation of the QED axial anomaly, the (ambiguous) definition of chiral currents, and the calculation of the chiral magnetic effect. We show that this model correctly contains the so-called consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly. Introducing net chirality through an axial chemical potential, we find a nonvanishing vector current only before including this counterterm. This seems to imply the absence of the chiral magnetic effect in this model. On the other hand, for a conventional quark chemical potential and large magnetic field, which is of interest in the physics of compact stars, we obtain a nontrivial result for the axial current that is in agreement with previous calculations and known exact results for QCD.Comment: 35 pages, 4 figures, v2: added comments about frequency-dependent conductivity at the end of section 4; references added; version to appear in JHE

Holographic chiral magnetic spiral

We study the ground state of baryonic/axial matter at zero temperature chiral-symmetry broken phase under a large magnetic field, in the framework of holographic QCD by Sakai-Sugimoto. Our study is motivated by a recent proposal of chiral magnetic spiral phase that has been argued to be favored against previously studied phase of homogeneous distribution of axial/baryonic currents in terms of meson super-currents dictated by triangle anomalies in QCD. Our results provide an existence proof of chiral magnetic spiral in strong coupling regime via holography, at least for large axial chemical potentials, whereas we don't find the phenomenon in the case of purely baryonic chemical potential.Comment: 24 pages, 15 figure

Abnormalities in autonomic function in obese boys at-risk for insulin resistance and obstructive sleep apnea.

Study objectivesCurrent evidence in adults suggests that, independent of obesity, obstructive sleep apnea (OSA) can lead to autonomic dysfunction and impaired glucose metabolism, but these relationships are less clear in children. The purpose of this study was to investigate the associations among OSA, glucose metabolism, and daytime autonomic function in obese pediatric subjects.MethodsTwenty-three obese boys participated in: overnight polysomnography; a frequently sampled intravenous glucose tolerance test; and recordings of spontaneous cardiorespiratory data in both the supine (baseline) and standing (sympathetic stimulus) postures.ResultsBaseline systolic blood pressure and reactivity of low-frequency heart rate variability to postural stress correlated with insulin resistance, increased fasting glucose, and reduced beta-cell function, but not OSA severity. Baroreflex sensitivity reactivity was reduced with sleep fragmentation, but only for subjects with low insulin sensitivity and/or low first-phase insulin response to glucose.ConclusionsThese findings suggest that vascular sympathetic activity impairment is more strongly affected by metabolic dysfunction than by OSA severity, while blunted vagal autonomic function associated with sleep fragmentation in OSA is enhanced when metabolic dysfunction is also present

Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems

A generic mechanism - networked buffering - is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems. \ud \u

Advances in small lasers

M.T.H was supported by an Australian Research council Future Fellowship research grant for this work. M.C.G. is grateful to the Scottish Funding Council (via SUPA) for financial support.Small lasers have dimensions or modes sizes close to or smaller than the wavelength of emitted light. In recent years there has been significant progress towards reducing the size and improving the characteristics of these devices. This work has been led primarily by the innovative use of new materials and cavity designs. This Review summarizes some of the latest developments, particularly in metallic and plasmonic lasers, improvements in small dielectric lasers, and the emerging area of small bio-compatible or bio-derived lasers. We examine the different approaches employed to reduce size and how they result in significant differences in the final device, particularly between metal- and dielectric-cavity lasers. We also present potential applications for the various forms of small lasers, and indicate where further developments are required.PostprintPeer reviewe

Algebraic conditions for additive functions over the reals and over finite fields

Let $C$ be an affine plane curve. We consider additive functions $f: K\rightarrow K$ for which $f(x)f(y)=0$, whenever $(x,y)\in C$. We show that if $K=\mathbb{R}$ and $C$ is the hyperbola with defining equation $xy=1$, then there exist nonzero additive functions with this property. Moreover, we show that such a nonzero $f$ exists for a field $K$ if and only if $K$ is transcendental over $\mathbb{Q}$ or over $\mathbb{F}_p$, the finite field with $p$ elements. We also consider the general question when $K$ is a finite field. We show that if the degree of the curve $C$ is large enough compared to the characteristic of $K$, then $f$ must be identically zero.Comment: 11 page