random Perturbation

The purpose of this Note is the determination of the in-plane homogenized strength domain of a "quasi-periodic" masonry under the assumption of infinitely resistant blocks connected by cohesionless Mohr-Coulomb interfaces. This masonry is obtained by introducing a random perturbation on the horizontal width of the blocks of a periodic running bond masonry. It is found that in some non-trivial cases the strength domain coincides exactly with that of the initial periodic masonry.

In this paper, we consider the class of α [γ,γ ] -generalized closed set in topological spaces and investigate some of their properties. We also present and study new separation axioms by using the notions of α-open and α-bioperations. Also, we analyze the relations with some well known separation axioms.

The large deviation principle obtained by Freidlin and Wentzell for measures associated with finite-dimensional diffusions is extended to measures given by stochastic evolution equations with non-additive random perturbations. The proof of the main result is adopted from the Priouret paper concerning finite-dimensional diffusions. Exponential tail estimates for infinite-dimensional stochastic convolutions are used as main tools.

Consider a two-dimensional continuous-time dynamical system, with an attracting xed point S. If the deterministic dynamics are perturbed by white noise (random perturbations) of strength , the system state will eventually leave the domain of attraction of S. We analyse the case when, as ! 0, the exit location on the boundary @ is increasingly concentrated near a saddle point H of the deterministic dynamics. We show using formal methods that the asymptotic form of the exit location distributionon @ is genericallynon-Gaussian and asymmetric, and classify the possible limiting distributions. A key role is played by a parameter , equal to the ratio j s(H)j= u(H) of the stable and unstable eigenvalues of the linearized deterministic ow at H. If < 1 then the exit location distribution is generically asymptotic as ! 0 to a Weibull distribution with shape parameter 2= , on the O(=2) lengthscale near H. If > 1 it is generically asymptotic to a distribution on the O(1=2) lengthscale, whose moments we compute. Our treatment employs both matched asymptotic expansions and stochastic analysis. As a byproduct of our treatment, we clarify the limitations of the traditional Eyring formula for the weak-noise exit time asymptotics.

We examine the effects of stochastic input currents on the firing behaviour of two coupled Type 1 or Type 2 neurons. In Hodgkin-Huxley model neurons with standard parameters, which are Type 2, in the bistable regime, synaptic transmission can initiate oscillatory joint spiking, but white noise can terminate it. In Type 1 cells (models), typified by a quadratic integrate and fire model, synaptic coupling can cause oscillatory behaviour in excitatory cells, but Gaussian white noise can again terminate it. We locally determine an approximate basin of attraction, A; of the periodic orbit and explain the firing behaviour in terms of the effects of noise on the probability of escape of trajectories from A:

We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a N-player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error for a given state and an agent. We then provide a characterization of solution points of these sub-problems that correspond to Nash equilibria of the underlying game and for this purpose, we derive a set of necessary and sufficient SG-SP (Stochastic Game-Sub-Problem) conditions. Using these conditions, we develop two actor-critic algorithms: OFF-SGSP (model-based) and ON-SGSP (model-free). Both algorithms use a critic that estimates the value function for a fixed policy and an actor that performs descent in the policy space using a descent direction that avoids local minima. We establish that both algorithms converge, in self-play, to the equilibria of a certain ordinary differential equation (ODE), whose stable limit points coincide with stationary NE of the underlying general-sum stochastic game. On a single state non-generic game (see Hart and Mas-Colell [2005]) as well as on a synthetic two-player game setup with 810, 000 states, we establish that ON-SGSP consistently outperforms NashQ [Hu and Wellman, 2003] and FFQ [Littman, 2001] algorithms.

A numerical study of the state and degree of polarization along single-polarization fibres has been carried out on the basis of M/311er-Stokes matrix approach and the mode coupling centre model. The general quasimonochromatic case is considered. Correspondence between polarization holding h-parameter and the mode coupling centres' parameters has been established. The spectral average process has been considered and a novel criterion has been proposed. Expressions for the degree of polarization along the fibre have been derived for the cases of guided mode excitation and nonpolarized input. The degree of polarization has been shown to tend to a saturation level which depends on the h-parameter, the differential mode attenuation Ac~ and the coherence length L~ in the fibre.

A method is developed for the optimal estimation of the parameters in a ji@ nonlinear model of flow in a channel. The data assimilated consist of values of the water surface elevation during a given interval. The method is based on the adjoint method of optimal control. It is shown that accurate ualues of the parameters can be estimated, and the estimates are stable with respect to random perturbations of the data provided that data from a suficient number of locations are available for assimilation.

Motivation: In prostate brachytherapy, intra-operative dosimetry optimization can be achieved through reconstruction of the implanted seeds from multiple C-arm fluoroscopy images. This process requires tracking of the C-arm poses. Methodology: We compute the pose of the C-arm relative to a stationary radiographic fiducial of known geometry. The fiducial was precisely fabricated. We register the 2D fluoroscopy image of the fiducial to a projected digitally reconstructed radiograph of the fiducial. The novelty of this approach is using image intensity alone without prior segmentation of the fluoroscopy image. Experiments and Results: Ground truth pose was established for each Carm image using a published and clinically tested segmentation-based method. Using 111 clinical C-arm images and ±10° and ±10 mm random perturbation around the ground-truth pose, the average rotation and translation errors were 0.62° (std=0.31°) and 0.73 mm (std= 0.55mm), respectively. Conclusion: Fully automated segmentation-free C-arm pose estimation was found to be clinically adequate on human patient data.

The compact representation of harmonic amplitudes in the sinusoidal coding of voiced speech is often achieved by the all-pole modeling of a spectral envelope. The perceptual accuracy of the representation may be enhanced by the use of frequency-scale warping prior to LP modeling. The effectiveness of a frequency warping function has been shown in previous work to depend on the underlying signal spectral shape as determined by phoneme quality as well as voice quality. This suggests the possibility of minimizing the perceived degradation due to LP modeling by adapting the warping function to the local signal spectrum. In this paper, an investigation is conducted to determine possible correlations between preferred warping condition and easily computable spectral cues. Experimental results are presented that demonstrate the advantage of adapting the warping function to the signal spectral envelope in the context of a sinusoidal speech coding scheme.

We consider a model of a square-wave bursting neuron residing in the regime of tonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting. The statistical properties of the emergent bursting patterns are studied in the present work. In particular, we identify two principal statistical regimes associated with the noise-induced bursting. In the first case, (type I) bursting oscillations are created mainly due to the fluctuations in the fast subsystem. In the alternative scenario, type II bursting, the random perturbations in the slow dynamics play a dominant role. We propose two classes of randomly perturbed slow-fast systems that realize type I and type II scenarios. For these models, we derive the Poincare maps. The analysis of the linearized Poincare maps of the randomly perturbed systems explains the distributions of the number of spikes within one burst and reveals their dependence on the small and control parameters present in the models. The mathematical analysis of the model problems is complemented by the numerical experiments with a generic Hodgkin-Huxley type model of a bursting neuron.

In previous work, EAs were shown to efficiently solve certain equations over partially commutative groups. The EAs depend on the values of several control parameters for success. Generally these values must be tuned to the structure of the equation or problem to be solved. Supposing suitable values are found, a natural concern is stability of the EA under random perturbation of its parameters. This work considers such a model of EA stability by defining neighbourhoods over EA parameter space and examining their properties. We define stability based upon Kolmogorov distance and analyse that distance between repeated random perturbations of parameters, forming a statistical indication of EA stability under parameter perturbation. We then analyse the model for the wider class of general EAs, meaning our model may serve as a framework for parameter optimisation and stability analysis.

We generalize a result from Volkov [Ann. Probab. 29 (2001) 66-91] and prove that, on a large class of locally finite connected graphs of bounded degree (G, ∼) and symmetric reinforcement matrices a = (a i,j) i,j ∈G , the vertex-reinforced random walk (VRRW) eventually localizes with positive probability on subsets which consist of a complete d-partite subgraph with possible loops plus its outer boundary. We first show that, in general, any stable equilibrium of a linear symmetric replicator dynamics with positive payoffs on a graph G satisfies the property that its support is a complete d-partite subgraph of G with possible loops, for some d ≥ 1. This result is used here for the study of VRRWs, but also applies to other contexts such as evolutionary models in population genetics and game theory. Next we generalize the result of Pemantle [Probab. Theory Related Fields 92 (1992) 117-136] and Benaïm [Ann. Probab. 25 (1997) 361-392] relating the asymptotic behavior of the VRRW to replicator dynamics. This enables us to conclude that, given any neighborhood of a strictly stable equilibrium with support S, the following event occurs with positive probability: the walk localizes on S ∪ ∂S (where ∂S is the outer boundary of S) and the density of occupation of the VRRW converges, with polynomial rate, to a strictly stable equilibrium in this neighborhood.

In the last years KWU-PWR plants have shown an increase in the neutron noise normalized root mean square. The frequency region of interest is below 1 Hz, so that thermohydraulic fluctuations seem to be one of the main reasons behind. In order to advance in understanding this phenomenon, the code S3K has been used to simulate temperature, flow and combined fluctuations at the core inlet. The S3K model used corresponds to Trillo Nuclear Power Plant which has a Flow Distribution Device, whose effect on the neutron noise levels has also been investigated. The results are compared with an analytical model and real plant data.

We consider online learning for episodic Markov decision processes (MDPs) with stochastic long-term budget constraints, which plays a central role in ensuring the safety of reinforcement learning. Here the loss function can vary arbitrarily across the episodes, whereas both the loss received and the budget consumption are revealed at the end of each episode. Previous works solve this problem under the restrictive assumption that the transition model of the MDP is known a priori and establish regret bounds that depend polynomially on the cardinalities of the state space S and the action space A. In this work, we propose a new upper confidence primal-dual algorithm, which only requires the trajectories sampled from the transition model. In particular, we prove that the proposed algorithm achieves O(L|S| |A|T) upper bounds of both the regret and the constraint violation, where L is the length of each episode. Our analysis incorporates a new high-probability drift analysis of Lagrange multiplier processes into the celebrated regret analysis of upper confidence reinforcement learning, which demonstrates the power of "optimism in the face of uncertainty" in constrained online learning.

We consider online learning for episodic stochastically constrained Markov decision processes (CMDP), which plays a central role in ensuring the safety of reinforcement learning. Here the loss function can vary arbitrarily across the episodes, whereas both the loss received and the budget consumption are revealed at the end of each episode. Previous works solve this problem under the restrictive assumption that the transition model of the Markov decision processes (MDP) is known a priori and establish regret bounds that depend polynomially on the cardinalities of the state space $\mathcal{S}$ and the action space $\mathcal{A}$. In this work, we propose a new \emph{upper confidence primal-dual} algorithm, which only requires the trajectories sampled from the transition model. In particular, we prove that the proposed algorithm achieves $\widetilde{\mathcal{O}}(L|\mathcal{S}|\sqrt{|\mathcal{A}|T})$ upper bounds of both the regret and the constraint violation, where $L$ is the length o...

The spin precession of positive muons in ultra-pure Nb single crystals of high perfection, cooled down in transverse magnetic fields 0.68B~: ~< B~ppl ~< 0.84B~: (B~: = upper critical field) from temperatures well above the superconducting transition temperature T~ = 9.25 K, has been investigated in the temperature range 2.6 K 4 T ~< 8.0 K. The experiments confirm the periodic field B(r) of triangular flux-line lattices as calculated from numerical solutions of the microscopic BCS-Gor'kov theory. The observed broadening of the van Hove singularities in the field distribution is discussed in terms of the combined effects of muon diffusion and random perturbations of the flux-line lattice.

System operators in the electricity industry purchase reserve capacity in a pro- curement auction in which suppliers o®er two-part bids, one part for making capacity avail- able and another part for supplying incremental energy when called. Key ingredients of an e±cient auction design are the scoring rule for comparing bids, and the settlement rule for paying accepted bids. We use the principle of incentive compatibility to establish that very simple rules su±ce. In particular, the scoring rule uses only the capacity part of the bid, and energy supplies are paid the spot price. This is the design adopted in California.

A limited domain cloud system-resolving model (CSRM) is used to simulate the interaction between cumulus convection and 2-dimensional linear gravity waves, a single horizontal wavenumber at a time. With a single horizontal wavenumber, soundings obtained from horizontal averages of the CSRM domain allow us to evolve the largescale wave equation and thereby model its interaction with cumulus convection. It is shown that convectively coupled waves with phase speeds of 8-13m/s can develop spontaneously in such simulations. The wave development is weaker at long wavelengths (> ~10000km). Waves at short wavelengths (~2000km) also appear weaker, but the evidence is less clear because of stronger influences from random perturbations. The simulated wave structures are found to change systematically with horizontal wavelength, and at horizontal wavelengths of 2000-3000km they exhibit many of the basic features of the observed 2-day waves. The simulated convectively coupled waves develop without feedbacks from radiative processes, surface fluxes, or wave radiation into the stratosphere, but vanish when moisture advection by the large-scale waves is disabled. A similar degree of vertical tilt is found in the simulated convective heating at all wavelengths considered, consistent with observational results. Implications of these results to conceptual models of convectively coupled waves are discussed. Besides being a useful tool for studying wave-convection interaction, the present approach also represents a useful framework for testing the ability of coarse-resolution CSRMs and Single Column Models in simulating convectively coupled waves.

A limited-domain cloud system–resolving model (CSRM) is used to simulate the interaction between cumulus convection and two-dimensional linear gravity waves, a single horizontal wavenumber at a time. With a single horizontal wavenumber, soundings obtained from horizontal averages of the CSRM domain allow the large-scale wave equation to be evolved, and thereby its interaction with cumulus convection is modeled. It is shown that convectively coupled waves with phase speeds of 8–13 m s−1 can develop spontaneously in such simulations. The wave development is weaker at long wavelengths (&gt;∼10 000 km). Waves at short wavelengths (∼2000 km) also appear weaker, but the evidence is less clear because of stronger influences from random perturbations. The simulated wave structures are found to change systematically with horizontal wavelength, and at horizontal wavelengths of 2000–3000 km they exhibit many of the basic features of the observed 2-day waves. The simulated convectively coupled ...

We analyze an anisotropic spin 1/2 two legs ladder in the presence of various type of random perturbations. The generic phase diagram for the pure system, in a way similar to spin one chains, consists of four phases: an Antiferromagnet, a Haldane gap or a Singlet phase (depending on the sign of interchain coupling) and two XY phases designated by XY1 and XY2. The effects of disorder depend crucially on whether it preserves XY symmetry (random field along z and random exchange) or not (random anisotropy or random XY fields). In all cases we computed the new phase diagram and the correlation length for the disordered system. The ladder exhibits a remarkable stability to disorder with XY symmetry. Not only the singlet phases but also the massless XY1 phase are totally unaffected by disorder in stark contrast with the single chain case. Even in the presence of an external magnetic field breaking the spin gap most of the phase diagram (including the XY point) remains unaffected by the disorder, again in opposition with the single chain case. This stabilization towards disorder is similar, albeit stronger, to the one occuring for fermionic ladders. On the other hand the XY2 phase is very strongly suppressed. Disorder breaking XY symmetry has much stronger effects and most of the phases at the exception of the singlet one are now destroyed. Interestingly, the disordered XY1 phase has a much shorter correlation length than the disordered XY2 phase contrarily with the case of perturbations preserving the rotation symmetry around the z axis. The ladder system is thus in fact much more anisotropic than its single chain counterpart with identical exchanges. Finally we examine the case of strong disorder or weak interchain exchange for XY symmetric disorder. Close to the isotropic point, when the interchain exchange is increased the system undergoes a transition between two decoupled disordered spin 1/2 chains to a singlet ladder unaffected by disorder. For more XY like systems, the transition occurs in two steps with a non disordered XY1 phase occuring between the decoupled chains and the singlet phase. Comparison with other disordered gapped systems such as spin one chains is discussed.

A well known result by Kilian (ACM 1988) asserts that general secure two computation (2PC) with statistical security, can be based on OT. Specifically, in the client-server model, where only one party-the client-receives an output, Kilian's result shows that given the ability to call an ideal oracle that computes OT, two parties can securely compute an arbitrary function of their inputs with unconditional security. Ishai et al. (EUROCRYPT 2011) further showed that this can be done efficiently for every two-party functionality in NC 1 in a single round. However, their results only achieve statistical security, namely, it is allowed to have some error in security. This leaves open the natural question as to which client-server functionalities can be computed with perfect security in the OT-hybrid model, and what is the round complexity of such computation. So far, only a handful of functionalities were known to have such protocols. In addition to the obvious theoretical appeal of the question towards better understanding secure computation, perfect, as opposed to statistical reductions, may be useful for designing secure multiparty protocols with high concrete efficiency, achieved by eliminating the dependence on a security parameter. In this work, we identify a large class of client-server functionalities f : X ×Y → {0, 1}, where the server's domain X is larger than the client's domain Y, that have a perfect reduction to OT. Furthermore, our reduction is 1-round using an oracle to secure evaluation of many parallel invocations of 1-out-of-2 bit OT, as done by Ishai et al. (EUROCRYPT 2011). Interestingly, the set of functions that we are able to compute was previously identified by Asharov (TCC 2014) in the context of fairness in two-party computation, naming these functions full-dimensional. Our result also extends to randomized non-Boolean functions f : X × Y → {0,. .. , k − 1} satisfying |X | > (k − 1) • |Y|.

We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation maps) a Borel probability non-atomic invariant measure exists for any map. We use this result to demonstrate that any interval translation map endowed with such a measure is metrically equivalent to an interval exchange map. Finally, we study the general case of piecewise continuous maps and prove a simple result on existence of an invariant measure provided all discontinuity points are wandering.

A numerical study of the state and degree of polarization along single-polarization fibres has been carried out on the basis of M/311er-Stokes matrix approach and the mode coupling centre model. The general quasimonochromatic case is considered. Correspondence between polarization holding h-parameter and the mode coupling centres' parameters has been established. The spectral average process has been considered and a novel criterion has been proposed. Expressions for the degree of polarization along the fibre have been derived for the cases of guided mode excitation and nonpolarized input. The degree of polarization has been shown to tend to a saturation level which depends on the h-parameter, the differential mode attenuation Ac~ and the coherence length L~ in the fibre.

A numerical study of the state and degree of polarization along single-polarization fibres has been carried out on the basis of M/311er-Stokes matrix approach and the mode coupling centre model. The general quasimonochromatic case is considered. Correspondence between polarization holding h-parameter and the mode coupling centres' parameters has been established. The spectral average process has been considered and a novel criterion has been proposed. Expressions for the degree of polarization along the fibre have been derived for the cases of guided mode excitation and nonpolarized input. The degree of polarization has been shown to tend to a saturation level which depends on the h-parameter, the differential mode attenuation Ac~ and the coherence length L~ in the fibre.

We present a novel technique for source authentication of a packet stream in a network, which intends to give guarantees that a specific network flow really comes from a claimed origin. This mechanism, named packet level authentication (PLA), can be an essential tool for addressing Denial of Service (DoS) attacks. Based on designated verifier signature schemes, our proposal is an appropriate and unprecedented solution applying digital signatures for DoS prevention. Our scheme does not rely on an expensive public-key infrastructure and makes use of light cryptography machinery that is suitable in the context of the Internet of Things (IoT). We analyze our proposed scheme as a defense measure considering known DoS attacks and present a formal proof of its resilience face to eventual adversaries. Furthermore, we compare our solution to already existent strategies, highlighting its advantages and drawbacks.

We describe a quantum voting scheme in which a ballot is an unknown quantum state for a voter. Such a ballot is hard to forge because it is difficult in principle to make a copy of an unknown quantum state. Moreover, our quantum voting scheme guarantees anonymity because the ballot can be randomized by voters. We also describe a distributed variant of our scheme that is robust against a dishonest administrator. This scheme should remain usable in the coming era of quantum computers, which are expected to break most existing cryptographic schemes. † NTT Information Sharing Platform Laboratories Musashino-shi, 80-8585 Japan Email: [email protected]

V predloženej práci je najprv predstavený zobecnený celočíselný autoregresný proces rádu p (GINAR(p)). Hlavným cieľom je opísanie celočíselného autoregresného procesu s náhodnými koeficientami (RCINAR(p)). K ich definovaniu je použitý zobecnený operátor.Ďalej sú odvodené základné charakteristiky GINAR(p) a RCINAR(p) procesov a uvedené podmienky pre ich stacionaritu a ergodicitu. Prezentujeme taktiež tri metódy odhadu paramaterov (Yule-Walker, Metóda podmienených najmenšíchštvorov, Zobecnená metóda momentov) a ich porovnanie na simuláciách vzhľadom k strednejštvorcovej chybe odhadu (MSE). Na záver je model RCINAR(3) použitý na reálnych dátach reprezentujúcich ročné počty zemetresení.

Complex responses observed in an experimental, nonlinear, moored structural system subjected to nearly periodic wave excitations are examined and compared with the simulations of a newly proposed independent-flow-field (IFF) model in this paper. Variations in wave heights are approximated by additive random perturbations to the dominant periodic component. Simulations show good agreement with the experimental results in both time and frequency domains. Noise effects on the experimental results including bridging and transition phenomena are investigated and interpreted by comparing with the simulations of its deterministic counterpart. Possible causes of a chaotic-like experimental result as previously observed are also inferred.

We present a statistical dynamical Kalman filter and compare its performance to deterministic ensemble square root and stochastic ensemble Kalman filters for error covariance modeling with applications to data assimilation. Our studies compare assimilation and error growth in barotropic flows during a period in 1979 in which several large scale atmospheric blocking regime transitions occurred in the Northern Hemisphere. We examine the role of sampling error and its effect on estimating the flow dependent growing error structures and the associated effects on the respective Kalman gains. We also introduce a Shannon entropy reduction measure and relate it to the spectra of the Kalman gain.

The effect of cycle burnup on the ex-core detector noise at the frequency of the pendular core barrel vibrations in the Ringhals-3 PWR core was investigated using a neutron noise simulator. The purpose of the investigations was to confirm or disprove a hypothesis raised by Sweeney et al. (1985) that fuel assembly vibrations could affect the ex-core detector noise and cause the corresponding peak in the auto power spectral density (APSD) to increase during the cycle due to the effects of fuel burnup, the change of boron concentration, flux redistribution etc. Numerical calculations were performed by modelling the vibrations of fuel assemblies at different locations in the core and calculating the induced neutron noise at three burnup steps. The APSD of the ex-core detector noise was evaluated with the assumption of vibrations either along a straight-line or along a random two-dimensional trajectory, with two different representations of the cross section perturbations caused by the vibrations. The results show the obvious effect of in-core fuel vibrations on the ex-core detector noise, but the monotonic increase of the APSD does not occur for all fuel elements, vibration types and cross section perturbation models. Such an increase of the of APSD occurs predominantly for peripheral assemblies with one of the perturbation models. However, assuming simultaneous vibrations of a number of fuel assemblies uniformly distributed over the core with random vibrations and the more realistic perturbation model, the effect of the peripheral assemblies will dominate and hence the surmised monotonic increase of the amplitude of the ex-core neutron noise during the cycle can be confirmed.

The dependence of the amplitude of the neutron noise in PWRs on the radial correlation length of the noise source, that is the inlet temperature fluctuations, is investigated. The motivation for this work comes from the recent observation that the noise amplitude has increased significantly in certain Spanish PWRs. The reason of this increase has not yet been satisfactorily identified, although there are a few assumptions. One new hypothesis, put forward in this paper, is that a coolant flow with more coherent characteristics, which has actually been observed, could explain the increase of the noise amplitude. A more coherent flow leads to a longer spatial (radial) correlation length of the inlet temperature fluctuations, which in turn, in case the APSD of the temperature noise is unchanged, will lead to the increase of the neutron noise APSD. The mechanism behind this phenomenon is the same as the reason of the failure of the traditional noise based method for the determination of the Moderator Temperature Coefficient (MTC), and is related to the characteristics of the spatially randomly distributed noise sources. In this paper the relationship between the radial correlation length of the inlet temperature fluctuations and the neutron noise amplitude is investigated quantitatively and the increase of the noise amplitude with the increased spatial correlation of the inlet temperature fluctuations is demonstrated.

We prove that the addition of an arbitrarily small random perturbation to a quantum spin system rounds a first order phase transition in the conjugate order parameter in d ≤ 2 dimensions, or for cases involving the breaking of a continuous symmetry in d ≤ 4. This establishes rigorously for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr.

A floating-point arithmetic algorithm designed for solving usual boolean operations (intersection, union, and difference) on arbitrary polyhedral meshes is described in this paper. It can be used in many pre-and post-processing applications in computational physics (e.g. cut-cell volume mesh generation or high order conservative remapping). The method provides conformal polyhedral meshes upon exit. The core idea is to triangulate the polygons, solve the intersections at the triangular level, reconstruct the polyhedra from the cloud of conformal triangles and then reaggregate their triangular faces to polygons. This approach offers a great flexibility regarding the admissible topologies: non-planar faces, concave faces or cells and some non-manifoldness are handled. The algorithm is described in details and some preliminary results are shown.

We investigate the performances and collective task-solving capabilities of complex networks of automata using the density problem as a typical case. We show by computer simulations that evolved Watts-Strogatz small-world networks have superior performance with respect to scale-free graphs of the Albert-Barabási type. Besides, Watts-Strogatz networks are much more robust in the face of transient uniformly random perturbations. This result differs from information diffusion on scale-free networks, where random faults are highly tolerated.

Using the theory of M/M/1 queues at stationarity, we provide criteria of stability (recurrence) for a stochastic inventory model with an observed selling rate and an optimally chosen buying rate. Optimality is based on the maximum gain under stability, where buying and selling prices, as well as shop-and stock-keeping costs are incorporated into the model. An important aspect is to achieve robustness of the stocking process by minimizing the fluctuation of the predicted gain. This robustness can be achieved by controlling intermediate transfer rates of the assumed stochastic tandem network. Stochastic simulations demonstrate the applicability of the stability criteria under several scenarios of differing intensities of perturbation.

In order to bound the condition number, we need an upper bound on the largest singular value in addition to the lower bound on the smallest that we derived last class. Since the largest singular value of A + G can be bounded by σn(A + G) = �A + G � ≤ �A � + �G� and we can’t really do much about �A�, the important thing to do is bound �G�. To start off with a weak but easy bound, we use the following simple lemma. Lemma 1. If ai denote the columns of the matrix A, then max �ai � ≤ �A � ≤ √ d max �ai� i i Proof. If ei denotes the vector with 1 in the ith component but 0’s everywhere else, then Aei = ai Hence the lefthand inequality is clear. For the other inequality, let x be a unit vector and write � � Ax = A xiei = xiai

Let A be an arbitrary matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large growth factor under Gaussian elimination without pivoting. By combining these results, we show that the smoothed precision necessary to solve Ax = b, for any b, using Gaussian elimination without pivoting is logarithmic. Moreover, when A is an all-zero square matrix, our results significantly improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997).

It is well known that the ensemble Kalman filter (EnKF) requires updating each ensemble member with perturbed observations in order to produce the proper analysis-error covariances. While increased accuracy in a mean square sense may be preferable in many applications, less accuracy might be preferable in other applications, especially if the variables being assimilated obey certain conservation laws. In land data assimilation, for instance, the update in soil moisture often produces a water balance residual, in the sense that the input water is not equal to output water. This study shows that suppressing the perturbation of observations in the EnKF and in the weakly constrained ensemble Kalman filter significantly improves the water balance residuals without significantly increasing the state errors.

We study the asymptotic behavior of solutions of differential equations dx,(t)/dt = A(y(t/&))x,(t), x,(O) = x0, where A(y), for y in a space Y, is a family of operators forming the generators of semigroups of bounded linear operators in a Hilbert space H, and y(t) is an ergodic jump Markov process in Y. Let A = l A(y)p(dy) where p(dy) is the ergodic distribution of y(t). We show that under appropriate conditions as E-+O the process x,(t) converges uniformly in probability to the nonrandom function X(t) which is the solution of the equation d%(t)/dt = .&C(t), X(0) = x,, and that C-"'(x,(t)-Z(t)) converges weakly to a Gaussian random function Z(t) for which a representation is obtained. Application to randomly perturbed partial differential equations with nonrandom initial and boundary conditions are included.

Let (X, ~) and (Y, qf) be two measurable spaces with X being a linear space. A system is determined by two functionsf(X): X~ Xand ~: Xx Y-. X, a (small) positive parameter e and a homogeneous Markov chain {Yn} in (Y, rC) which describes random perturbations. States of the system, say { x,~ r X, n = 0, l,...}, are determined by the iteration relations: x,~ + t = f(x~,) + tga(x~, Yn + ~) for n I> 0, where ~o = Xo is given. Here we study the asymptotic behavior of the solution x~, as e ~ 0 and n ~ oo under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.

The entropy of a dynamical system S' on a hyperbolic attractor with respect to the Bowen-Ruelle-Sina) measure is obtained as a limit of entropy characteristics of small random perturbations x' of S'. Both the case of perturbations only in some neighborhood of an attractor and global perturbations of a flow with hyperbolic attracting sets are considered.