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April 26, 2019Happy Friday, everyone! Today Carter and Keri discuss Walter Strickland (an SJW convergence operative in the evangelical community) and worker agency and the morality of sweatshops. Then Keri waits patiently for Carter to finish ranting about Keynesianism and Q1's 3.2% GDP growth.YouTube link to video version of this episode:https://youtu.be/IG7dTyzj5NM

Thank you for choosing Star Wars Alliance for all of your Star Wars News and Reviews. Time stamps:Convergence Spoiler Review 11:21Follow us on Twitter! •Star Wars Alliance- @starwrsalliance•Katie- @sliceofkatie•Clay- @FanboyClaySTAR WARS Alliance is apart of the GEEK ULTIMATE ALLIANCE NETWORK.We have 8 shows across the week •A Slice of Film (Bi-weekly Mondays): •World's Finest True Believers (Monthly Last Sunday): •Ranger Alliance (Bi-weekly Monday): •DC Alliance (Tuesdays): •Superhero Discussions (Wednesdays): •Star Wars Alliance (Thursdays): •Marvel Alliance(Fridays): •A Walk Through The Multiverse (Bi-weekly Saturdays): Remember to subscribe to the GeekVerse YouTube channel and set notifications to \"ALL\" to catch us when we go live every Wednesday night at 7pm EST. •https://www.youtube.com/GeekVersePodcastPlease consider joining our Patreon to support us and everyone at the GUA•https://www.patreon.com/guanetwork

When you cross paths with your past...

Source: https://www.twitch.tv/videos/1987652159 Uploader: NadiVonMandalore

Source: https://www.twitch.tv/videos/2000274677 Uploader: NadiVonMandalore

This is highlights of the lecture givin by amanda of rocketboom.com fame.I shot theis for the group while at the conference.amanda is dicussing the different aspects of vloging with the crowd.

This is highlights of the lecture givin by amanda of rocketboom.com fame.I shot theis for the group while at the conference.amanda is dicussing the different aspects of vloging with the crowd.

New customer-facing developments at fueling stations engage customers at convenience retailers.

A model for oblique convergence between plates of lithosphere is proposed in which at least a fraction of slip parallel to the plate margin results in transcurrent movements on a nearly vertical fault which is located on the continental side of a zone of plate consumption. In an extreme case of complete decoupling only the component of slip normal to the plate margin can be inferred from underthrusting. Recent movements in the western Sunda region provide the most convincing evidence for decoupling of slip, which in this region is thought to be oblique to the plate margin. A speculative model for convergence along the margins of the Philippine Sea is constructed from an inferred direction of oblique slip in the Philippine region. This model requires that the triple point formed by the junction of the Japanese and Izu-Bonin trenches and the Nankai trough migrate along the Sagami trough.

The Twilight Saga: Harmonic Convergence Wiki dumped with WikiTeam tools.

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I explore the Globalist Links that the ASMIN and its members have in different Councils and I look at the upcoming protests (from September 20, 2023 onward) and how the many opposing ideals creates a chaotic arena that pushes the Ordo Ab Chao (Order Out of Chaos) Agenda. Relevant Videos: https://www.youtube.com/watch?v=FW0BTcHT5Qk&t=2461s https://www.youtube.com/watch?v=0q8yxPi-GWU&t=35s https://www.youtube.com/watch?v=NBybM9DvCzk&t=1419s https://www.youtube.com/watch?v=thUuMe625T0&t=869s Links Used: https://issuu.com/ctm-magazine/docs/expanded_web_edition_150th_ctm https://rumble.com/v3il2ku-this-is-a-secret-recording-of-a-joint-meeting-held-september-16th.html https://www.westernstandard.news/features/canadian-parental-rights-activist-says-upcoming-protest-will-show-people-s-anger/article_763ab160-55de-11ee-b38c-9783321de680.html https://twitter.com/FernMayo84/status/1702380150896083142?s=20 https://twitter.com/DDelvez/status/1704206720283578644?s=20 https://rumble.com/v3grjuq-restored-republic-via-a-gcr-update-as-of-september-11-2023.html https://thelovephone.com/ https://www.youtube.com/watch?v=QxOyfewxpeY https://www.newswire.ca/news-releases/northernnations-cooperative-working-to-provide-550-indigenous-groups-with-products-to-help-prevent-the-further-spread-of-covid-19-808507377.html https://www.newswire.ca/news-releases/ucw-bestows-matt-vickers-with-honorary-doctorate-recognizing-his-contributions-to-canada-s-indigenous-peoples-849429850.html https://www.mattvickers.com/ https://ca.linkedin.com/in/matthew-matt-vickers-b1375b8 https://www.flickr.com/photos/21728045@N08/11157300905/in/photostream/ https://www.asminoftheborealforest.com/membership-information https://www.asminoftheborealforest.com/asmin-of-the-boreal-forest https://www.linkedin.com/in/francis-louis-charbonneau-jr-ba-mba-msc-613208a?challengeSource=AgHAUfXbWr6mIQAAAYn1T6BhtDX4qkzvn4_4zngv79S10u9ONiVZU4bHw5keezM&challegeType=AgE0h7G08g-bugAAAYn1T6BkV-bUmALl6Jktt3kbOTggvMSFT8nQ72c&memberId=AgHHa3nCVy8gQAAAAYn1T6BosVXDsePSL8WTIPKvz5h7NG0&recognizeDevice=AgF_pF7YO5D04gAAAYn1T6BrQ4OudzQ77NIXkSoHeG5I3c8KinFB&challengeSource=AgGdkrxx8Cg2LwAAAYn5-CJR5LbW7WPQKsMes-k-NfmS888C-d9CrnvYnHQndlE&challegeType=AgH3RFrRo9LG9QAAAYn5-CJUpMMYrA1mb8nbcAwnkKW4nAYDp7dNZ3Q&memberId=AgHcck4DJTu0EAAAAYn5-CJYXSW6th5lpyllkkvnSy-SnmQ&recognizeDevice=AgHsEofULZceyAAAAYn5-CJbGRUh4k0tuFhOpyGHG9AyJA6lNyfw&challengeSource=AgGz4uk4u1p4hAAAAYn5-GuRGc3PN-HA-yPiEsbLTBAysxwwQhRiOGFJ-Sg32ks&challegeType=AgHdTM2l-u1n4QAAAYn5-GuURfcoqPvfYc-AID_c6NaM3VBD_Y0k3KE&memberId=AgE7CNvOmbPugQAAAYn5-GuXwYjL1S3BO9BqCZD9JFQyV2M&recognizeDevice=AgGz6Blomu5UnwAAAYn5-Guay72D08jy0Ek2vnocVA2iFnKZz8Mh&challengeId=AQEnWB4bTgiaWQAAAYojQU-2BGOa-jj4gzybjMYaIbUDbKqMKjEZgiryRf9hZpPekflkSTIR00raU8zAd8wRAFdfhflt4xVxaQ&submissionId=6c44683a-7310-7e17-ea01-7f9f765ce63c&challengeSource=AgEw5AM4hkIOIQAAAYojQdKdZEVzVI1Gil_CdpJV1gbziYQ9NnWafLdGcBvE-x0&challegeType=AgGve9R2ywDSiQAAAYojQdKgPoavfu1aN45CySiCbJWYWdN9RU7Zvas&memberId=AgEf90RfIP88VgAAAYojQdKjcahesk3qbDT-ZN9aChUSPLk&recognizeDevice=AgG6qDMi3GSqowAAAYojQdKmni6-4tBCz7lDh791JvOxiHMAwSot https://www.asminofturtleisland.org/team-3 https://www.votealoha.org/kaulia https://www.linkedin.com/in/donald-kaulia-41268210 https://www.linkedin.com/in/randy-unter-92747035?trk=public_profile_recommendations https://business.ucdenver.edu/centers/health-administration/health-administration-industry-partners https://operationdisclosure1.blogspot.com/2020/07/new-us-political-party-aloha-aina.html https://www.classmates.com/people/sir-daniel-w.-bilbruck/7592848927 https://robertmcangusgroup.tumblr.com/post/101156729565/sir-daniel-bilbruck-senior-advisor-to-the-board-of https://www.linkedin.com/in/sir-daniel-bilbruck-2736708 https://www.iso.org/sdgs.html https://www.mentorworks.ca/blog/government-funding/what-are-rdas/ https://ised-isde.canada.ca/site/innovation-better-canada/en https://ised-isde.canada.ca/site/ised/en/canadas-regional-development-agencies https://laclabiche.albertacf.com/about/about-us https://laclabiche.albertacf.com/about/board-of-directors https://speakerscanada.com/keynote-speaker/peter-cardinal/ https://ca.linkedin.com/in/peter-cardinal-468a1a3b https://gotoinnovation.eu/eu-funds/ https://gotoinnovation.eu/partners/ https://gotoinnovation.eu/ https://gotoinnovation.eu/advisors-board/ https://ca.linkedin.com/in/arthur-jefford-gwayak-bikwak-01042115 https://www.asminofturtleisland.org/about-1

June 4, 1987

psychedelic depiction of a breakthrough experience.

Burning libraries, walled cities, and Da Vinci, oh my!  Craig Cormick joins us live at CONvergence to talk about  The Shadow Master  from Angry Robot Books.  We talk writing alternate history, the library of Alexandria, and so much more! We hope you enjoy the episode! Feel free to shoot us an email at skiffyandfanty [at] gmail [dot] com! You can also leave a comment  on our website .  Our intro music is "Time Flux" by ( Revolution Void ) /  CC BY 3.0 .

Consider the initial boundary value problem for Burgers' equation. It is shown that its solutions converge, in time, to a unique steady state. The speed of the convergence depends on the boundary conditions and can be exponentially slow. Methods to speed up the rate of convergence are also discussed.

This paper is concerned with the convergence study of Newton's method on the image set generated by the Micheletti group. At first we review the structure of first and second derivatives of shape functions and present a new proof of the structure theorem for second (shape) derivatives. Then we examine a quotient group and compute its tangent space and relate it to the shape derivative. In the second part of the paper we introduce a class of so-called approximate normal functions using reproducing kernels. The approximate normal functions are then used to define a Newton method. Under suitable assumptions we are able to show the convergence of the Newton method in the Micheletti group. Finally we verify our findings in a number of numerical experiments.

A lacunary sequence is an increasing integer sequence $\theta=(k_r)$ such that $k_r-k_{r-1}\rightarrow \infty$ as $r\rightarrow \infty.$ In this article we introduce arithmetic statistically convergent sequence space $ASC$ and lacunary arithmetic statistically convergent sequence space $ASC_{\theta}$ and study some inclusion properties between the two spaces. Finally we introduce lacunary arithmetic statistical continuity and establish some interesting results.

Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to the inherent variance in the gradient computation. To accelerate the convergence, some variance-reduced stochastic gradient algorithms, e.g., proximal stochastic variance-reduced gradient (Prox-SVRG) algorithm, have recently been proposed to solve strongly convex problems. Under the strongly convex condition, these variance-reduced stochastic gradient algorithms achieve a linear convergence rate. However, many machine learning problems are convex but not strongly convex. In this paper, we introduce Prox-SVRG and its projected variant called Variance-Reduced Projected Stochastic Gradient (VRPSG) to solve a class of non-strongly convex optimization problems widely used in machine learning. As the main technical contribution of this paper, we show that both VRPSG and Prox-SVRG achieve a linear convergence rate without strong convexity. A key ingredient in our proof is a Semi-Strongly Convex (SSC) inequality which is the first to be rigorously proved for a class of non-strongly convex problems in both constrained and regularized settings. Moreover, the SSC inequality is independent of algorithms and may be applied to analyze other stochastic gradient algorithms besides VRPSG and Prox-SVRG, which may be of independent interest. To the best of our knowledge, this is the first work that establishes the linear convergence rate for the variance-reduced stochastic gradient algorithms on solving both constrained and regularized problems without strong convexity.

We develope a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the $ L^p $-distance between the solution process of an SDE and an arbitrary It\^o process, which we view as a perturbation of the solution process of the SDE, by the $ L^q $-distances of the differences of the local characteristics for suitable $ p, q > 0 $. As application of our perturbation theory, we establish strong convergence rates for numerical approximations of a class of SODEs with non-globally monotone coefficients. As another application of our perturbation theory, we prove strong convergence rates for spectral Galerkin approximations of solutions of semilinear SPDEs with non-globally monotone nonlinearities including Cahn-Hilliard-Cook type equations and stochastic Burgers equations. Further applications of the perturbation theory include the regularity of solutions of SDEs with respect to the initial values and small-noise analysis for ordinary and partial differential equations.

Max stable laws are limit laws of linearly normalized partial maxima of independent identically distributed random variables. Saeb (2014) proves that the Renyi entropy of order b (b > 1) of linear normalized maximum of iid random variables with continuous differentiable density is convergent to the Renyi entropy of order b of the max stable laws. In this paper, we study the rate of convergence result for Renyi entropy for linearly normalized partial maxima.

In this monograph, we develop results on global existence and convergence of solutions to abstract gradient flows on Banach spaces for a potential function that obeys the Lojasiewicz-Simon gradient inequality. We prove a Lojasiewicz-Simon gradient inequality for the Yang-Mills energy functional over closed, smooth Riemannian manifolds of arbitrary dimension and apply the resulting framework to prove new results for the gradient flow equation for the Yang-Mills energy functional on a principal bundle, with compact Lie structure group, over a closed, smooth Riemannian manifolds, including the following. If the initial connection is close enough to a local minimum of the Yang-Mills energy functional, in a norm sense when the base manifold has arbitrary dimension or in an energy sense when the base manifold has dimension four, then the Yang-Mills gradient flow exists for all time and converges to a Yang-Mills connection. If the initial connection is allowed to have arbitrary energy but we restrict to the setting of a Hermitian vector bundle over a compact, complex, Hermitian (but not necessarily Kaehler) surface and the initial connection has curvature of type (1,1), then the Yang-Mills gradient flow exists for all time, though bubble singularities may (and in certain cases must) occur in the limit as time tends to infinity.

We investigate a mixed boundary value problem for the stationary heat transfer equation in a thin layer with a mid hypersurface $\mathcal{C}$ in $\mathbb{R}^3$ with the boundary. The main object is to trace what happens in $\Gamma$-limit when the thickness of the layer converges to zero. The limit Dirichlet BVP for the Laplace-Beltrami equation on the surface is described explicitly and we show how the Neumann boundary conditions in the initial BVP transform in the $\Gamma$-limit. For this we apply the variational formulation and the calculus of G\"unter's tangential differential operators on a hypersurface and layers, which allow global representation of basic differential operators and of corresponding boundary value problems in terms of the standard Euclidean coordinates of the ambient space $\mathbb{R}^n$.

We establish a connection between the $L^2$ norm of sums of dilated functions whose $j$th Fourier coefficients are $\mathcal{O}(j^{-\alpha})$ for some $\alpha \in (1/2,1)$, and the spectral norms of certain greatest common divisor (GCD) matrices. Utilizing recent bounds for these spectral norms, we obtain sharp conditions for the convergence in $L^2$ and for the almost everywhere convergence of series of dilated functions.

On the Convergence of Infinite Series of Analytic Functions. Webb, H Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Math. or Phys. Character (1896-1934). 1905-01-01. 204:481–497

In several variables, we prove the pointwise convergence of multiresolution expansions to the distributional point values of tempered distributions and distributions of superexponential growth. The article extends and improves earlier results by G. G. Walter and B. K. Sohn and D. H. Pahk that were shown in one variable. We also provide characterizations of the quasiasymptotic behavior of distributions at finite points and discuss connections with $\alpha$-density points of measures.

This article is from The British Journal of Ophthalmology , volume 98 . Abstract Aim: This paper presents Convergence Insufficiency Symptom Survey (CISS) and orthoptic findings in a sample of typical young adults who considered themselves to have normal eyesight apart from weak spectacles. Methods: The CISS questionnaire was administered, followed by a full orthoptic evaluation, to 167 university undergraduate and postgraduate students during the recruitment phase of another study. The primary criterion for recruitment to this study was that participants ‘felt they had normal eyesight’. A CISS score of ≥21 was used to define ‘significant’ symptoms, and convergence insufficiency (CI) was defined as convergence ≥8 cm from the nose with a fusion range

As part of providing wireline access to the 5G Core (5GC), deployed wireline networks carry user data between 5G residential gateways and the 5G Access Gateway Function (AGF). The encapsulation method specified in this document supports the multiplexing of traffic for multiple PDU sessions within a VLAN-delineated access circuit, permits legacy equipment in the data path to inspect certain packet fields, carries 5G QoS information associated with the packet data, and provides efficient encoding. It achieves this by specific points of similarity with the Point-to-Point Protocol over Ethernet (PPPoE) data packet encapsulation (RFC 2516).

As part of providing wireline access to the 5G Core (5GC), deployed wireline networks carry user data between 5G residential gateways and the 5G Access Gateway Function (AGF). The encapsulation method specified in this document supports the multiplexing of traffic for multiple PDU sessions within a VLAN-delineated access circuit, permits legacy equipment in the data path to inspect certain packet fields, carries 5G QoS information associated with the packet data, and provides efficient encoding. It achieves this by specific points of similarity with the Point-to-Point Protocol over Ethernet (PPPoE) data packet encapsulation (RFC 2516).

We recently introduced a novel replica-exchange scheme in which an individual replica can sample from states encountered by other replicas at any previous time by way of a global configuration database, enabling the fast propagation of relevant states through the whole ensemble of replicas. This mechanism depends on the knowledge of global thermodynamic functions which are measured during the simulation and not coupled to the heat bath temperatures driving the individual simulations. Therefore, this setup also allows for a continuous adaptation of the temperature set. In this paper, we will review the new scheme and demonstrate its capability. The method is particularly useful for the fast and reliable estimation of the microcanonical temperature T(U) or, equivalently, of the density of states g(U) over a wide range of energies.

This paper deals with studying vague convergence of random measures of the form $\mu_{n}=\sum_{i=1}^{n} p_{i,n} \delta_{\theta_i}$, where $(\theta_i)_{1\le i \le n}$ is a sequence of independent and identically distributed random variables with common distribution $\Pi$, $(p_{i,n})_{1 \le i \le n}$ are random variables chosen according to certain procedures and are independent of $(\theta_i)_{i \geq 1}$ and $\delta_{\theta_i}$ denotes the Dirac measure at $\theta_i$. We show that $\mu_{n}$ converges vaguely to $\mu=\sum_{i=1}^{\infty} p_{i} \delta_{\theta_i}$ if and only if $\mu^{(k)}_{n}=\sum_{i=1}^{k} p_{i,n} \delta_{\theta_i}$ converges vaguely to $\mu^{(k)}=\sum_{i=1}^{k} p_{i} \delta_{\theta_i}$ for all $k$ fixed. The limiting process $\mu$ plays a central role in many areas in statistics, including Bayesian nonparametric models. A finite approximation of the beta process is derived from the application of this result. A simulated example is incorporated, in which the proposed approach exhibits an excellent performance over several existing algorithms.

"A May Day Convergence" Sunday, April 30, 10:50 am On May 1st, it would appear that everything is converging at the same moment, whether it be the international worker's holiday, the Beltane festival, or a desperate call for help. Rev. Millie Phillips, Affiliated Community Minister; Mari Magaloni Ramos, Worship Associate; Reiko Oda Lane, Organist; UUSF Choir led by Mark Sumner, Music Director Shulee Ong, Camera; Eric Shackelford, Camera; Jonathan Silk, Communications Director; Santana Gonzalez-Gomez, Chat Moderator; Thomas Brown, Sexton; Athena Papsadakos, Flowers; Linda Messner, Head Usher

This article is from PLoS Genetics , volume 10 . Abstract Light is one of the most important environmental cues regulating multiple aspects of plant growth and development, and abscisic acid (ABA) is a plant hormone that plays important roles during many phases of the plant life cycle and in plants' responses to various environmental stresses. How plants integrate the external light signal with endogenous ABA pathway for better adaptation and survival remains poorly understood. Here, we show that BBX21 (also known as SALT TOLERANCE HOMOLOG 2), a B-box (BBX) protein previously shown to positively regulate seedling photomorphogenesis, is also involved in ABA signaling. Our genetic data show that BBX21 may act upstream of several ABA INSENSITIVE (ABI) genes and ELONGATED HYPOCOTYL 5 (HY5) in ABA control of seed germination. Previous studies showed that HY5 acts as a direct activator of ABI5 expression, and that BBX21 interacts with HY5. We further demonstrate that BBX21 negatively regulates ABI5 expression by interfering with HY5 binding to the ABI5 promoter. In addition, ABI5 was shown to directly activate its own expression, whereas BBX21 negatively regulates this activity by directly interacting with ABI5. Together, our study indicates that BBX21 coordinates with HY5 and ABI5 on the ABI5 promoter and that these transcriptional regulators work in concert to integrate light and ABA signaling in Arabidopsis thaliana.

This article is from Frontiers in Computational Neuroscience , volume 8 . Abstract The cerebellum is known to play a critical role in learning relevant patterns of activity for adaptive motor control, but the underlying network mechanisms are only partly understood. The classical long-term synaptic plasticity between parallel fibers (PFs) and Purkinje cells (PCs), which is driven by the inferior olive (IO), can only account for limited aspects of learning. Recently, the role of additional forms of plasticity in the granular layer, molecular layer and deep cerebellar nuclei (DCN) has been considered. In particular, learning at DCN synapses allows for generalization, but convergence to a stable state requires hundreds of repetitions. In this paper we have explored the putative role of the IO-DCN connection by endowing it with adaptable weights and exploring its implications in a closed-loop robotic manipulation task. Our results show that IO-DCN plasticity accelerates convergence of learning by up to two orders of magnitude without conflicting with the generalization properties conferred by DCN plasticity. Thus, this model suggests that multiple distributed learning mechanisms provide a key for explaining the complex properties of procedural learning and open up new experimental questions for synaptic plasticity in the cerebellar network.

This article is from Frontiers in Computational Neuroscience , volume 8 . Abstract The cerebellum is known to play a critical role in learning relevant patterns of activity for adaptive motor control, but the underlying network mechanisms are only partly understood. The classical long-term synaptic plasticity between parallel fibers (PFs) and Purkinje cells (PCs), which is driven by the inferior olive (IO), can only account for limited aspects of learning. Recently, the role of additional forms of plasticity in the granular layer, molecular layer and deep cerebellar nuclei (DCN) has been considered. In particular, learning at DCN synapses allows for generalization, but convergence to a stable state requires hundreds of repetitions. In this paper we have explored the putative role of the IO-DCN connection by endowing it with adaptable weights and exploring its implications in a closed-loop robotic manipulation task. Our results show that IO-DCN plasticity accelerates convergence of learning by up to two orders of magnitude without conflicting with the generalization properties conferred by DCN plasticity. Thus, this model suggests that multiple distributed learning mechanisms provide a key for explaining the complex properties of procedural learning and open up new experimental questions for synaptic plasticity in the cerebellar network.

This document describes a mechanism for link-state routing protocols that prevents local transient forwarding loops in case of link failure. This mechanism proposes a two-step convergence by introducing a delay between the convergence of the node adjacent to the topology change and the network-wide convergence.

IEEE Std 802.16 is an air interface specification for fixed and mobile Broadband Wireless Access Systems. Service-specific convergence sublayers to which upper-layer protocols interface are a part of the IEEE 802.16 MAC (Medium Access Control). The Packet convergence sublayer (CS) is used for the transport of all packet- based protocols such as Internet Protocol (IP) and IEEE 802.3 LAN/MAN CSMA/CD Access Method (Ethernet). IPv6 packets can be sent and received via the IP-specific part of the Packet CS. This document specifies the addressing and operation of IPv6 over the IP-specific part of the Packet CS for hosts served by a network that utilizes the IEEE Std 802.16 air interface. It recommends the assignment of a unique prefix (or prefixes) to each host and allows the host to use multiple identifiers within that prefix, including support for randomly generated interface identifiers. [STANDARDS-TRACK]

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Convergence 1986: Volume 19 , Issue Index. Digitized from IA1519307-04 . Previous issue: sim_convergence_1987_20_3-4 . Next issue: sim_convergence_1988_21_index .

Convergence 1996: Volume 29 , Issue Index. Digitized from IA1519307-05 . Next issue: sim_convergence_1996_29_1 .

In sufficiently large gaps and electric fields, discharge streamers do branch. In [Arrayas et al., PRL 88, 174502 (2002)], we observed streamer branching numerically within a deterministic particle density model and explained it as a Laplacian instability of a thin space charge layer. Our numerical results were criticized in [Kulikovsky, PRL 89, 229401 (2002)]. We here present an adaptive grid refinement method for streamer simulations, and we carry out the first conclusive investigation on the effect of the numerical grid on streamer branching in different fields. On stepwise finer grids the branching time converges, hence streamer branching is for the first time predicted quantitatively.

In sufficiently large gaps and electric fields, discharge streamers do branch. In [Arrayas et al., PRL 88, 174502 (2002)], we observed streamer branching numerically within a deterministic particle density model and explained it as a Laplacian instability of a thin space charge layer. Our numerical results were criticized in [Kulikovsky, PRL 89, 229401 (2002)]. We here present an adaptive grid refinement method for streamer simulations, and we carry out the first conclusive investigation on the effect of the numerical grid on streamer branching in different fields. On stepwise finer grids the branching time converges, hence streamer branching is for the first time predicted quantitatively.

In sufficiently large gaps and electric fields, discharge streamers do branch. In [Arrayas et al., PRL 88, 174502 (2002)], we observed streamer branching numerically within a deterministic particle density model and explained it as a Laplacian instability of a thin space charge layer. Our numerical results were criticized in [Kulikovsky, PRL 89, 229401 (2002)]. We here present an adaptive grid refinement method for streamer simulations, and we carry out the first conclusive investigation on the effect of the numerical grid on streamer branching in different fields. On stepwise finer grids the branching time converges, hence streamer branching is for the first time predicted quantitatively.

We address the question of a Berry Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial sums in an operator-valued free central limit theorem and the Cauchy transform of the limiting operator-valued semicircular element.

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of Strohmer and Vershynin for systems of linear equations, we show that, under appropriate probability distributions, the linear rates of convergence (in expectation) can be bounded in terms of natural linear-algebraic condition numbers for the problems. We relate these condition measures to distances to ill-posedness, and discuss generalizations to convex systems under metric regularity assumptions.

In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the logarithmic homogeneity of self-concordant barrier function, which must have {\em negative curvature}. We propose a new path-following predictor-corrector scheme, which work only in the dual space. It is based on an easily computable gradient proximity measure, which ensures an automatic transformation of the global linear rate of convergence to the local superlinear one under some mild assumptions. Our step-size procedure for the predictor step is related to the maximum step size maintaining feasibility. As the optimal solution set is approached, our algorithm automatically tightens the neighborhood of the central path proportionally to the current duality gap.

We analyze the convergence rate of a simplified version of a popular Gibbs sampling method used for statistical discovery of gene regulatory binding motifs in DNA sequences. This sampler satisfies a very strong form of ergodicity (uniform). However, we show that, due to multimodality of the posterior distribution, the rate of convergence often decreases exponentially as a function of the length of the DNA sequence. Specifically, we show that this occurs whenever there is more than one true repeating pattern in the data. In practice there are typically multiple such patterns in biological data, the goal being to detect the most well-conserved and frequently-occurring of these. Our findings match empirical results, in which the motif-discovery Gibbs sampler has exhibited such poor convergence that it is used only for finding modes of the posterior distribution (candidate motifs) rather than for obtaining samples from that distribution. Ours are some of the first meaningful bounds on the convergence rate of a Markov chain method for sampling from a multimodal posterior distribution, as a function of statistical quantities like the number of observations.

We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form $Au_t(t,x) + B(u_{xx}(t,x)+ru_x(t,x))+Cu(t,x) = f(t,x)$, where $A,B,C\in\R^{n,n}$ and the matrix $A$ is singular. We prove that under certain conditions the temporal convergence order of the fully discrete scheme depends on the time index of the partial differential-algebraic equation. In particular, fractional orders of convergence in time are encountered. Furthermore we show that the fully discrete scheme suffers an order reduction caused by the boundary conditions. Numerical examples confirm the theoretical results.

This paper considers a cross-layer optimization problem driven by multi-timescale stochastic exogenous processes in wireless communication networks. Due to the hierarchical information structure in a wireless network, a mixed timescale stochastic iterative algorithm is proposed to track the time-varying optimal solution of the cross-layer optimization problem, where the variables are partitioned into short-term controls updated in a faster timescale, and long-term controls updated in a slower timescale. We focus on establishing a convergence analysis framework for such multi-timescale algorithms, which is difficult due to the timescale separation of the algorithm and the time-varying nature of the exogenous processes. To cope with this challenge, we model the algorithm dynamics using stochastic differential equations (SDEs) and show that the study of the algorithm convergence is equivalent to the study of the stochastic stability of a virtual stochastic dynamic system (VSDS). Leveraging the techniques of Lyapunov stability, we derive a sufficient condition for the algorithm stability and a tracking error bound in terms of the parameters of the multi-timescale exogenous processes. Based on these results, an adaptive compensation algorithm is proposed to enhance the tracking performance. Finally, we illustrate the framework by an application example in wireless heterogeneous network.