Curvature in Noncommutative Geometry

Our understanding of the notion of curvature in a noncommutative setting has progressed substantially in the past ten years. This new episode in noncommutative geometry started when a Gauss-Bonnet theorem was proved by Connes and Tretkoff for a curved noncommutative two torus. Ideas from spectral geometry and heat kernel asymptotic expansions suggest a general way of defining local curvature invariants for noncommutative Riemannian type spaces where the metric structure is encoded by a Dirac type operator. To carry explicit computations however one needs quite intriguing new ideas. We give an account of the most recent developments on the notion of curvature in noncommutative geometry in this paper.Comment: 76 pages, 8 figures, final version, one section on open problems added, and references expanded. Appears in "Advances in Noncommutative Geometry - on the occasion of Alain Connes' 70th birthday

Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson–Walker Cosmologies

We obtain an explicit formula for the full expansion of the spectral action on Robertson–Walker spacetimes, expressed in terms of Bell polynomials, using Brownian bridge integrals and the Feynman–Kac formula. We then apply this result to the case of multifractal Packed Swiss Cheese Cosmology models obtained from an arrangement of Robertson–Walker spacetimes along an Apollonian sphere packing. Using Mellin transforms, we show that the asymptotic expansion of the spectral action contains the same terms as in the case of a single Robertson–Walkerspacetime, but with zeta-regularized coefficients, given by values at integers of the zeta function of the fractal string of the radii of the sphere packing, as well as additional log-periodic correction terms arising fromthe poles (off the real line) of this zeta function

The effect of massage therapy on the severity of labor in primiparous women

چکیده: زمینه و هدف: درد زایمان شدیدترین دردی است که اغلب زنان آن را تجربه می کنند. با استفاده از روش های نوین و حمایتی کاهش درد زایمان می توان زایمان را به یک اتفاق خوشایند و لذت بخش تبدیل نمود. مطالعه حاضر با هدف تعیین تاثیر ماساژ درمانی بر شدت درد زایمان در زنان نخست زا انجام شده است. روش بررسی: در یک مطالعه کار آزمایی بالینی 60 خانم حامله نخست زا در حال زایمان از بیمارستان های مهدیه و هدایت شهر تهران به روش نمونه گیری آسان انتخاب و به صورت تصادفی به دو گروه شاهد و ماساژ درمانی (مورد) تقسیم شدند. گروه شاهد از مراقبت های روتین بدون هیچ مداخله ای و گروه مورد ماساژ درمانی با استفاده از تکنیک ماساژ درمانی افلوراج انجام شد. شدت درد قبل از مداخله (ابتدای فاز فعال) و بعد از مداخله در دیلاتاسیون های 4، 8 و 10 سانتی متر سرویکس با استفاده از مقیاس سنجش درد VAS (Visual analogue scale) اندازه گیری شد. طول مدت مرحله اول و دوم و نوع زایمان در هر دو گروه، مورد بررسی قرار گرفت. داده های هر دو گروه با استفاده از آزمونهای آماری کای دو و t مستقل با یکدیگر مقایسه شدند. یافته ها: بر اساس نتایج قبل از مداخله بین دو گروه از نظر شدت درد اختلاف معنی داری مشاهده نشد. میانگین شدت درد به ترتیب در گروه ماساژ و شاهد در ابتدای فاز فعال 07/1±88/5 و 39/1±75/6 (01/0

The term a_4 in the heat kernel expansion of noncommutative tori

We consider the Laplacian associated with a general metric in the canonical conformal structure of the noncommutative two torus, and calculate a local expression for the term a4 that appears in its corresponding small-time heat kernel expansion. The final formula involves one variable functions and lengthy two, three and four variable functions of the modular automorphism of the state that encodes the conformal perturbation of the flat metric. We confirm the validity of the calculated expressions by showing that they satisfy a family of conceptually predicted functional relations. By studying these functional relations abstractly, we derive a partial differential system which involves a natural action of cyclic groups of order 2, 3 and 4 and a flow in parameter space. We discover symmetries of the calculated expressions with respect to the action of the cyclic groups. In passing, we show that the main ingredients of our calculations, which come from a rearrangement lemma and relations between the derivatives up to order 4 of the conformal factor and those of its logarithm, can be derived by finite differences from the generating function of the Bernoulli numbers and its multiplicative inverse. We then shed light on the significance of exponential polynomials and their smooth fractions in understanding the general structure of the noncommutative geometric invariants appearing in the heat kernel expansion. As an application of our results we obtain the a4 term for noncommutative four tori which split as products of two tori. These four tori are not conformally flat and the a4 term gives a first hint of the Riemann curvature and the higher-dimensional modular structure

Spectral action for Bianchi type-IX cosmological models

In this paper we prove a rationality phenomena for the coefficients of the heat kernel expansion of the Dirac-Laplacian of Bianchi IX cosmological models. Due the complexities arising from the anisotropic nature of the model, we present a novel method of writing the heat coefficients as Wodzicki resiudes of certain Laplacians and then provide an elegant proof of the rationality result. That is, we show that each coefficient is described by a several variable polynomial with rational coefficients of the cosmic expansion factors and their higher derivatives of a certain order. This result confirms the arithmetic nature of the complicated terms in the expansion

Motives and periods in Bianchi IX gravity models

In this paper we show that the heat coefficients of the Dirac-Laplacian of SU(2)-invariant Bianchi IX metrics are periods of motives of complements in affine spaces of unions of quadrics and hyperplanes

A high-current, high-voltage power supply with special output current waveform for APS injector synchrotron dipole magnets

This paper describes a high-voltage, high-current power supply for the injector synchrotron dipole magnets at APS. In order to reset the dipole magnets in each cycle two different current waveforms are suggested. The first current waveform consists of three sections, namely: dc-reset, linear ramp, and recovery sections where injection is done ``on the fly``. The second current waveform consists of six different sections, dc-reset, transition to injection level, injection flat level, parabolic, linear ramp and recovery sections. The effect of such waveforms on the beam is discussed and the power supply limitations to follow such waveforms are given. The power supply limitations are due to the power components and control loops. The reference for the current loop is generated by a DAC which is discussed

Ultrathin graphene-based membrane with precise molecular sieving and ultrafast solvent permeation

Graphene oxide (GO) membranes continue to attract intense interest due to their unique molecular sieving properties combined with fast permeation. However, their use is limited to aqueous solutions because GO membranes appear impermeable to organic solvents, a phenomenon not yet fully understood. Here, we report efficient and fast filtration of organic solutions through GO laminates containing smooth two-dimensional (2D) capillaries made from large (10-20 μm) flakes. Without modification of sieving characteristics, these membranes can be made exceptionally thin, down to â 1/410 nm, which translates into fast water and organic solvent permeation. We attribute organic solvent permeation and sieving properties to randomly distributed pinholes interconnected by short graphene channels with a width of 1 nm. With increasing membrane thickness, organic solvent permeation rates decay exponentially but water continues to permeate quickly, in agreement with previous reports. The potential of ultrathin GO laminates for organic solvent nanofiltration is demonstrated by showing >99.9% rejection of small molecular weight organic dyes dissolved in methanol. Our work significantly expands possibilities for the use of GO membranes in purification and filtration technologies

Positive End-Expiratory Pressure may alter breathing cardiovascular variability and baroreflex gain in mechanically ventilated patients

<p>Abstract</p> <p>Background</p> <p>Baroreflex allows to reduce sudden rises or falls of arterial pressure through parallel RR interval fluctuations induced by autonomic nervous system. During spontaneous breathing, the application of positive end-expiratory pressure (PEEP) may affect the autonomic nervous system, as suggested by changes in baroreflex efficiency and RR variability. During mechanical ventilation, some patients have stable cardiorespiratory phase difference and high-frequency amplitude of RR variability (HF-RR amplitude) over time and others do not. Our first hypothesis was that a steady pattern could be associated with reduced baroreflex sensitivity and HF-RR amplitude, reflecting a blunted autonomic nervous function. Our second hypothesis was that PEEP, widely used in critical care patients, could affect their autonomic function, promoting both steady pattern and reduced baroreflex sensitivity.</p> <p>Methods</p> <p>We tested the effect of increasing PEEP from 5 to 10 cm H2O on the breathing variability of arterial pressure and RR intervals, and on the baroreflex. Invasive arterial pressure, ECG and ventilatory flow were recorded in 23 mechanically ventilated patients during 15 minutes for both PEEP levels. HF amplitude of RR and systolic blood pressure (SBP) time series and HF phase differences between RR, SBP and ventilatory signals were continuously computed by complex demodulation. Cross-spectral analysis was used to assess the coherence and gain functions between RR and SBP, yielding baroreflex-sensitivity indices.</p> <p>Results</p> <p>At PEEP 10, the 12 patients with a stable pattern had lower baroreflex gain and HF-RR amplitude of variability than the 11 other patients. Increasing PEEP was generally associated with a decreased baroreflex gain and a greater stability of HF-RR amplitude and cardiorespiratory phase difference. Four patients who exhibited a variable pattern at PEEP 5 became stable at PEEP 10. At PEEP 10, a stable pattern was associated with higher organ failure score and catecholamine dosage.</p> <p>Conclusions</p> <p>During mechanical ventilation, stable HF-RR amplitude and cardiorespiratory phase difference over time reflect a blunted autonomic nervous function which might worsen as PEEP increases.</p