Subdiffusion in hair bundle dynamics: The role of protein conformational fluctuations

The detection of sound signals in vertebrates involves a complex network of different mechano-sensory elements in the inner ear. An especially important element in this network is the hair bundle, an antenna-like array of stereocilia containing gated ion channels that operate under the control of one or more adaptation motors. Deflections of the hair bundle by sound vibrations or thermal fluctuations transiently open the ion channels, allowing the flow of ions through them, and producing an electrical signal in the process, eventually causing the sensation of hearing. Recent high frequency (0.1-10 kHz) measurements by Kozlov et al. Proc. Natl. Acad. Sci. U. S. A. 109, 2896 (2012)] of the power spectrum and the mean square displacement of the thermal fluctuations of the hair bundle suggest that in this regime the dynamics of the hair bundle are subdiffusive. This finding has been explained in terms of the simple Brownian motion of a filament connecting neighboring stereocilia (the tip link), which is modeled as a viscoelastic spring. In the present paper, the diffusive anomalies of the hair bundle are ascribed to tip link fluctuations that evolve by fractional Brownian motion, which originates in fractional Gaussian noise and is characterized by a power law memory. The predictions of this model for the power spectrum of the hair bundle and its mean square displacement are consistent with the experimental data and the known properties of the tip link. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4768902]

Duty cycling and power management with a network of energy harvesting sensors

In this paper, we study duty cycling and power management in a network of energy harvesting sensor (EHS) nodes. We consider a one-hop network, where K EHS nodes send data to a destination over a wireless fading channel. The goal is to find the optimum duty cycling and power scheduling across the nodes that maximizes the average sum data rate, subject to energy neutrality at each node. We adopt a two-stage approach to simplify the problem. In the inner stage, we solve the problem of optimal duty cycling of the nodes, subject to the short-term power constraint set by the outer stage. The outer stage sets the short-term power constraints on the inner stage to maximize the long-term expected sum data rate, subject to long-term energy neutrality at each node. Albeit suboptimal, our solutions turn out to have a surprisingly simple form: the duty cycle allotted to each node by the inner stage is simply the fractional allotted power of that node relative to the total allotted power. The sum power allotted is a clipped version of the sum harvested power across all the nodes. The average sum throughput thus ultimately depends only on the sum harvested power and its statistics. We illustrate the performance improvement offered by the proposed solution compared to other naive schemes via Monte-Carlo simulations.

Interference planning for multicell OFDM downlink

In this paper we consider the downlink of an OFDM cellular system. The objective is to maximise the system utility by means of fractional frequency reuse and interference planning. The problem is a joint scheduling and power allocation problem. Using gradient scheduling scheme, the above problem is transformed to a problem of maximising weighted sum-rate at each time slot. At each slot, an iterative scheduling and power allocation algorithm is employed to address the weighted sum-rate maximisation problem. The power allocation problem in the above algorithm is a nonconvex optimisation problem. We study several algorithms that can tackle this part of the problem. We propose two modifications to the above algorithms to address practical and computational feasibility. Finally, we compare the performance of our algorithm with some existing algorithms based on certain achieved system utility metrics. We show that the practical considerations do not affect the system performance adversely.

Solid-liquid transition in polydisperse Lennard-Jones systems

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (delta(t) similar or equal to 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at delta similar or equal to 0.09 in case of T* = 1.0, phi = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at delta similar or equal to 0.10 (just beyond the solid-liquid transition density at T* = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal

The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.

Insertion Reactions of Six-Membered Cyclopalladated N,N `,N `'-Triarylguanidine, Pd{kappa(2)(C,N)-C6H3Me-3(NHC(NHAr)(=NAr))-2)(mu-Br)](2) (Ar=2-MeC6H4) with PhCC C-C(O)OR (R = Me and Et): A Gateway to Second Orthopalladation through Novel Rearrangements

The reaction of Pd{kappa(2)(C,N)-C6H3Me-3-(NHC(NHAr)(=NAr))-2}(mu-Br)](2) (Ar = 2-MeC6H4; 1) with 4 equiv of PhC C-C(O)OMe in CH2Cl2 afforded Pd{kappa(2)(C,N)-C(Ph)=C(C(O)OMe)C(Ph)=C(C(O)-OMe)C6H3Me-3(N=C(NH Ar)(2))-2}Br] (Ar = 2-MeC6H4; 2) in 70% yield, and the aforementioned reaction carried out with 10 equiv of PhC C-C(O)OR (R = Me, and Et) afforded an admixture of two regioisomers of Pd{kappa(3)(N,C,O)-O=C(OR)-C5Ph3(C(O)OR)C(C(O)OR)C6H3Me-3(N=C(NHAr)( 2))- 2}Br] (Ar = 2-MeC6H4; R = Me (3a/3b), Et (4a/4b)) in 80 and 87% yields, respectively. In one attempt, the minor regioisomer, 4b, was isolated from the mixture in 6% yield by fractional crystallization. Palladacycles 3a/3b and 4a/4b, upon stirring in CH2Cl2/MeCN (1/1, v/v) mixture at ambient condition for S days, afforded Pd{eta(3)-allyl,(KN)-N-1)-C-5(C(O)OR)(2)Ph3C-(C(O)OR)C6H3Me-3(N=C(NH Ar)(2))(-2)}Br] (Ar = 2-MeC6H4; R = Me (5a/5b), Et (6a/6b)) in 94 and 93% yields, respectively. Palladacycles 3a/3b and 4a/4b, upon reaction with AgOTf in CH2CH2/Me2C(O) (1/1, v/v) mixture at ambient temperature for 15 min, afforded Pd{kappa(3)(N,C,O)-O=C(OR)C5Ph3(C(O)OR)C(C(O)OR)C6H3Me-3(N=C(NHAr)(2 ))-2}(OTf)] (Ar = 2-MeC6H4; R = Me (7a/7b), Et (8a/8b)) in 79 and 77% yields, respectively. Palladacycles 7a/7b and 8a/ 8b, upon reflux in PhC1 separately for 6 h, or palladacycles 5a/5b and 6a/6b, upon treatment with AgOTf in CH2Cl2/Me2C(O) (7/3, v/v) mixture for 15 min, afforded Pd{(eta(2)-Ph)C5Ph2(C(O)OR)kappa(2)(C,N)-C(C(O)OR)C6H3Me-3(N=C(NHAr) (2))-2}(OTf)] (Ar = 2-MeC6H4; R = Me (9a/9h), Et (10a/10b)) in >= 87% yields. Palladacycles 9a/9b, upon stirring in MeCN in the presence of excess NaOAc followed by crystallization of the reaction mixture in the same solvent, afforded Pd{kappa(3)(N,C,C)-(C6H4)C5Ph2(C(O)OMe)(2)C(C(O)OMe)(2)C6H3Me-3(N=C( NHAr)(2))-2}(NCMe)] (Ar = 2-MeC6H4; 11a/11b) in 82% yield. The new palladacycles were characterized by analytical, IR, and NMR (H-1 and C-13) spectroscopic techniques, and the molecular structures of 2, 3a, 4a, 4b, 5a, 6a, 7a, 9a, 10a, and 11a-d(3) were determined by single crystal X-ray diffraction. The frameworks in the aforementioned palladacycles, except that present in 2, are unprecedented. Plausible pathways for the formation of new palladacycles and the influence of the guanidine unit in 1, substituents in alkynes, reaction conditions, and electrophilicity of the bromide and the triflate upon the frameworks of the insertion products have been discussed.

Topological analysis of electron density and the electrostatic properties of isoniazid: an experimental and theoretical study

Isoniazid (isonicotinohydrazide) is an important first-line antitubercular drug that targets the InhA enzyme which synthesizes the critical component of the mycobacterial cell wall. An experimental charge-density analysis of isoniazid has been performed to understand its structural and electronic properties in the solid state. A high-resolution single-crystal X-ray intensity data has been collected at 90 K. An aspherical multipole refinement was carried out to explore the topological and electrostatic properties of the isoniazid molecule. The experimental results were compared with the theoretical charge-density calculations performed using CRYSTAL09 with the B3LYP/6-31G** method. A topological analysis of the electron density reveals that the Laplacian of electron density of the N-N bond is significantly less negative, which indicates that the charges at the b.c.p. (bond-critical point) of the bond are least accumulated, and so the bond is considered to be weak. As expected, a strong negative electrostatic potential region is present in the vicinity of the O1, N1 and N3 atoms, which are the reactive locations of the molecule. The C-H center dot center dot center dot N, C-H center dot center dot center dot O and N-H center dot center dot center dot N types of intermolecular hydrogen-bonding interactions stabilize the crystal structure. The topological analysis of the electron density on hydrogen bonding shows the strength of intermolecular interactions.

UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

This paper deals with the Schrodinger equation i partial derivative(s)u(z, t; s) - Lu(z, t; s) = 0; where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.

Binaural Signal Processing Motivated Generalized Analytic Signal Construction and AM-FM Demodulation

Binaural hearing studies show that the auditory system uses the phase-difference information in the auditory stimuli for localization of a sound source. Motivated by this finding, we present a method for demodulation of amplitude-modulated-frequency-modulated (AM-FM) signals using a ignal and its arbitrary phase-shifted version. The demodulation is achieved using two allpass filters, whose impulse responses are related through the fractional Hilbert transform (FrHT). The allpass filters are obtained by cosine-modulation of a zero-phase flat-top prototype halfband lowpass filter. The outputs of the filters are combined to construct an analytic signal (AS) from which the AM and FM are estimated. We show that, under certain assumptions on the signal and the filter structures, the AM and FM can be obtained exactly. The AM-FM calculations are based on the quasi-eigenfunction approximation. We then extend the concept to the demodulation of multicomponent signals using uniform and non-uniform cosine-modulated filterbank (FB) structures consisting of flat bandpass filters, including the uniform cosine-modulated, equivalent rectangular bandwidth (ERB), and constant-Q filterbanks. We validate the theoretical calculations by considering application on synthesized AM-FM signals and compare the performance in presence of noise with three other multiband demodulation techniques, namely, the Teager-energy-based approach, the Gabor's AS approach, and the linear transduction filter approach. We also show demodulation results for real signals.

Upper Bounds on the Size of Grain-Correcting Codes

In this paper, we revisit the combinatorial error model of Mazumdar et al. that models errors in high-density magnetic recording caused by lack of knowledge of grain boundaries in the recording medium. We present new upper bounds on the cardinality/rate of binary block codes that correct errors within this model. All our bounds, except for one, are obtained using combinatorial arguments based on hypergraph fractional coverings. The exception is a bound derived via an information-theoretic argument. Our bounds significantly improve upon existing bounds from the prior literature.

Unusual eigenvalue spectrum and relaxation in the Levy-Ornstein-Uhlenbeck process

We consider the rates of relaxation of a particle in a harmonic well, subject to Levy noise characterized by its Levy index mu. Using the propagator for this Levy-Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue spectrum of the associated Fokker-Planck operator has the form (n + m mu)nu where nu is the force constant characterizing the well, and n, m is an element of N. If mu is irrational, the eigenvalues are all nondegenerate, but rational mu can lead to degeneracy. The maximum degeneracy is shown to be 2. The left eigenfunctions of the fractional Fokker-Planck operator are very simple while the right eigenfunctions may be obtained from the lowest eigenfunction by a combination of two different step-up operators. Further, we find that the acceptable eigenfunctions should have the asymptotic behavior vertical bar x vertical bar(-n1-n2 mu) as vertical bar x vertical bar -> infinity, with n(1) and n(2) being positive integers, though this condition alone is not enough to identify them uniquely. We also assert that the rates of relaxation of LOUP are determined by the eigenvalues of the associated fractional Fokker-Planck operator and do not depend on the initial state if the moments of the initial distribution are all finite. If the initial distribution has fat tails, for which the higher moments diverge, one can have nonspectral relaxation, as pointed out by Toenjes et al. Phys. Rev. Lett. 110, 150602 (2013)].

AN OPTIMUM SHRINKAGE ESTIMATOR BASED ON MINIMUM-PROBABILITY-OF-ERROR CRITERION AND APPLICATION TO SIGNAL DENOISING

We address the problem of designing an optimal pointwise shrinkage estimator in the transform domain, based on the minimum probability of error (MPE) criterion. We assume an additive model for the noise corrupting the clean signal. The proposed formulation is general in the sense that it can handle various noise distributions. We consider various noise distributions (Gaussian, Student's-t, and Laplacian) and compare the denoising performance of the estimator obtained with the mean-squared error (MSE)-based estimators. The MSE optimization is carried out using an unbiased estimator of the MSE, namely Stein's Unbiased Risk Estimate (SURE). Experimental results show that the MPE estimator outperforms the SURE estimator in terms of SNR of the denoised output, for low (0 -10 dB) and medium values (10 - 20 dB) of the input SNR.

Charge density distribution and electrostatic interactions of ethionamide: an inhibitor of the enoyl acyl carrier protein reductase (inhA) enzyme of Mycobacterium tuberculosis

An experimental charge density analysis of an anti-TB drug ethionamide was carried out from high resolution X-ray diffraction at 100 K to understand its charge density distribution and electrostatic properties. The experimental results were validated from periodic theoretical charge density calculations performed using CRYSTAL09 at the B3LYP/6-31G** level of theory. The electron density rho(bcp)(r) and the Laplacian of electron density del(2)(rho bcp)(r) of the molecule calculated from both the methods display the charge density distribution of the ethionamide molecule in the crystal field. The electrostatic potential map shows a large electropositive region around the pyridine ring and a large electronegative region at the vicinity of the thiol atom. The calculated experimental dipole moment is 10.6D, which is higher than the value calculated from theory (8.2D). The topological properties of C-H center dot center dot center dot S, N-H center dot center dot center dot N and N-H center dot center dot center dot S hydrogen bonds were calculated, revealing their strength. The charge density analysis of the ethionamide molecule determined from both the experiment and theory gives the topological and electrostatic properties of the molecule, which allows to precisely understand the nature of intra and intermolecular interactions.

Heat kernels on the AdS(2) cone and logarithmic corrections to extremal black hole entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over ZN orbifolds of higher-dimensional spheres and hyperboloids.

The Tetrablock as a Spectral Set

The tetrablock, roughly speaking, is the set of all linear fractional maps that map the open unit disc to itself. A formal definition of this inhomogeneous domain is given below. This paper considers triples of commuting bounded operators (A,B,P) that have the tetrablock as a spectral set. Such a triple is named a tetrablock contraction. The motivation comes from the success of model theory in another inhomogeneous domain, namely, the symmetrized bidisc F. A pair of commuting bounded operators (S,P) with Gamma as a spectral set is called a Gamma-contraction, and always has a dilation. The two domains are related intricately as the Lemma 3.2 below shows. Given a triple (A, B, P) as above, we associate with it a pair (F-1, F-2), called its fundamental operators. We show that (A,B,P) dilates if the fundamental operators F-1 and F-2 satisfy certain commutativity conditions. Moreover, the dilation space is no bigger than the minimal isometric dilation space of the contraction P. Whether these commutativity conditions are necessary, too, is not known. what we have shown is that if there is a tetrablock isometric dilation on the minimal isometric dilation space of P. then those commutativity conditions necessarily get imposed on the fundamental operators. En route, we decipher the structure of a tetrablock unitary (this is the candidate as the dilation triple) and a tertrablock isometry (the restriction of a tetrablock unitary to a joint invariant sub-space). We derive new results about r-contractions and apply them to tetrablock contractions. The methods applied are motivated by 11]. Although the calculations are lengthy and more complicated, they beautifully reveal that the dilation depends on the mutual relationship of the two fundamental operators, so that certain conditions need to be satisfied. The question of whether all tetrablock contractions dilate or not is unresolved.