Downloads & Free Reading Options - Results

This is the second iteration of the Medieval defensive anti-cavalry tile with openlock connections. This is also known as Cheval de Frise. This has been modified to have the improved interface openlock 6.0 template which has different ways of connecting. Also the redesign has spikes going in only one direction with a different spike arrangement. I wanted more variety in appearance in my games. These could be moved and anchored at different locations to prevent cavalry charges or to help block a breach in another barrier. It is a good tile for war game type play by adding movable or stationary obstacles. The first iteration is found here. https://www.thingiverse.com/thing:2430558

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we uniformly sample polynomially many samples from the (exponentially large) state space. This way, the complexity of our algorithm becomes polynomial in the size of the fMDP description length. We prove that the algorithm is convergent. We also derive an upper bound on the difference between our approximate solution and the optimal one, and also on the error introduced by sampling. We analyze various projection operators with respect to their computation complexity and their convergence when combined with approximate value iteration.

Episode 17 of ChannelFourteen's Third World Gaming Podcast

an older version of my personal website, conor.bio

We extend the definition of an orbit portrait to the context of non-autonomous iteration, both for the combinatorial version involving collections of angles and for the dynamic version involving external rays where combinatorial portraits can be realized by the dynamics associated with sequences of polynomials with suitably uniformly bounded degrees and coefficients. We show that, in the case of sequences of polynomials of constant degree, the portraits which arise are eventually periodic which is somewhat similar to the classical theory of polynomial iteration. However, if the degrees of the polynomials in the sequence are allowed to vary, one can obtain portraits with complementary arcs of irrational length which are fundamentally different from the classical ones.

We consider a general class of total cost Markov decision processes (MDP) in which the one-stage costs can have arbitrary signs, but the sum of the negative parts of the one-stage costs is finite for all policies and all initial states. We refer to this class as the General Convergence (GC for short) total cost model, and we study the convergence of value iteration for the GC model, in the Borel MDP framework with universally measurable policies. Our main results include: (i) convergence of value iteration when starting from certain functions above the optimal cost function; (ii) convergence of transfinite value iteration starting from zero, in the special case where the optimal cost function is nonnegative; and (iii) partial convergence of value iteration starting from zero, for a subset of initial states. These results extend several previously known results about the convergence of value iteration for either positive costs problems or GC total cost problems. In particular, the first result on convergence of value iteration from above extends a theorem of van der Wal for the GC model. The second result relates to Maitra and Sudderth's analysis of transfinite value iteration for the positive costs model. It suggests connections between the two total cost models when the optimal cost function is nonnegative, and it leads to additional results on the convergence of ordinary non-transfinite value iteration, with a suitably defined dynamic programming operator, for finite state or finite control GC problems. The third result on partial convergence of value iteration is motivated by Whittle's bridging condition for the positive costs model, and provides a novel extension of the bridging condition to the GC model, where there are no sign constraints on the costs.

This study offers a new swarm-based metaheuristic: random-guided optimizer (RGO). RGO has novel mechanics in shifting the random motion into a guided motion strategy during the iteration. In RGO, the iteration is divided into three equal size phases. In the first phase, the unit walks randomly inside the search space to tackle the local optimal problem earlier. In the second phase, each unit uses a unit selected randomly among the population as a reference in conducting the guided motion. In the third phase, each unit conducts guided motion toward or surpasses the best unit. Through simulation, RGO successfully finds the acceptable solution for 23 benchmark functions. Moreover, RGO successfully finds the global optimal solution for four functions: Branin, Goldstein-Price, Six Hump Camel, and Schwefel 2.22. RGO also outperforms slime mold algorithm (SMA), pelican optimization algorithm (POA), golden search optimizer (GSO), and northern goshawk optimizer (NGO) in solving 12, 20, 12, and 1 function consecutively. In the future, improvement can be made by transforming RGO into solid multiple-phase strategy without losing its identity as a metaheuristic with multiple strategy in every iteration.

Quantum states of the electromagnetic field are of considerable importance, finding potential application in various areas of physics, as diverse as solid state physics, quantum communication and cosmology. In this paper we introduce the concept of truncated states obtained via iterative processes (TSI) and study its statistical features, making an analogy with dynamical systems theory (DST). As a specific example, we have studied TSI for the doubling and the logistic functions, which are standard functions in studying chaos. TSI for both the doubling and logistic functions exhibit certain similar patterns when their statistical features are compared from the point of view of DST. A general method to engineer TSI in the running-wave domain is employed, which includes the errors due to the nonidealities of detectors and photocounts.

Let each vertex of a graph G = (V(G), E(G)) be given one of two colors, say, "black" and "white". Let Z denote the (initial) set of black vertices of G. The color-change rule converts the color of a vertex from white to black if the white vertex is the only white neighbor of a black vertex. The set Z is said to be a zero forcing set of G if all vertices of G will be turned black after finitely many applications of the color-change rule. The zero forcing number of G is the minimum of |Z| over all zero forcing sets Z \subseteq V (G). Zero forcing parameters have been studied and applied to the minimum rank problem for graphs in numerous articles. We define the iteration index of a zero forcing set of a graph G to be the number of (global) applications of the color-change rule required to turn all vertices of G black; this leads to a new graph invariant, the iteration index of G - it is the minimum of iteration indices of all minimum zero forcing sets of G. We present some basic properties of the iteration index and discuss some preliminary results on certain graphs.

Character design in MMO games draws players in and gets them invested in both the game world and their own characters. Designing compelling, unique races and characters while making them a cohesive part of the world’s lore is critical for creating an immersive game experience. Join ArenaNet character artists, including Kristen Perry, as they dive deep into character and racial design in Guild Wars 2. Using specific examples, the artists will take a look at what it takes to create compelling character designs, discuss design challenges and how they overcame them, and provide insight into their creative process. Panelist: Kristen Perry [Artist,  Website ]

This is my 3rd iteration of this design. I am finally at a stage where I would say it is done. The router is slimmed compared to previous versions, and only need Nema 17 stepper motors now. The build uses affordable components available in many hardware stores, making it quite cheap! Files, pictures, BOM and other details can be found in my instructable here: https://www.instructables.com/id/Low-Budget-CNC/ Also a video can be seen here: https://www.youtube.com/watch?v=MWKC1xnfwgw

In The News: Betcha didn't know that the US military in Afghanistan is in day four of an offensive bolstered by Pakistani troops into Waziristan. The 101st Airborne is working the Afghan side of the border. 33 alleged 'rebels' killed. Details. The Iraqi oil ministry opens bidding on production contracts for 6 major oilfields. Hey! I thought it was OUR oil under THEIR sand. The oilfield service contracts are still hung up in the Iraqi parliament partially because we happened to kill one of president al-Maliki's cousins last week, and he's not... really... happy... with us right now. More from Juan Colle @ Informed Comment: McClatchy reports that the diplomatic crisis between the al-Maliki government and the US military over the killing of his cousin is deepening. The US undertook a raid in Janaja in Karbala, which was supposedly under Iraqi military control, without any coordination with Iraqis and killed a security guard, who turns out to be a cousin of PM al-Maliki and the bodyguard of his sister. The US says it was conducting the raid against a "special group," their terminology for a Shiite cell they believe to receive aid or training from Iran. This incident makes little sense on the surface. Why would the US raid the home town of the PM without forewarning him? Why kill this relative? Al-Maliki is a leader of the Da'wa Party. Did the US military suspect that a Da'wa cell in Janaja was targeting US troops in the Shiite south, with Iranian encouragement? If so, it would make sense of why they did not warn al-Maliki their operation was coming. But if this scenario is anywhere close to reality, it raises questions about al-Maliki's control of his branch of the Da'wa, and about the character of the party (which is still run on a cadre basis as a set of covert cells rather than being a proper, popular political party). In any case, the incident looks set to sour Iraqi-American relations even further. In Full @ Informed Comment The US is going to arm the Mexican Drug Enforcement army... enquiring minds want to know: "Will all of that military equipment end up being sold, traded to, and stolen by, the drug lords?" Unintended side-effects: Amsterdam outlaws the use of tobacco in public places... adversely affecting the hashish/marijuana culture because the Dutch like to mix tobacco with their weed. BTW, they think we Americans are heathens for 'smoking it raw'... After the commentary, Quicksilver Messenger Service asks "What About Me?", courtesy of the respective artists and KPIG radio Freedom California Earth Oh, and don't forget to "Obey" --30-- "All The News You Never Knew You Needed To Know ...Until Now." Travus T. Hipp - Cabale News Service Recorded by The Buffalo In Da' Midst @ My Buffalo River Home Courtesy of Cabale New Service and KPIG Radio , Popout player below the fold in the "Notes".

customized with 3D Slash!

CS 61A - Spring 08 - The Structure and Interpretation of Computer Programs Instructor Brian Harvey Introduction to programming and computer science. This course exposes students to techniques of abstraction at several levels: (a) within a programming language, using higher-order functions, manifest types, data-directed programming, and message-passing; (b) between programming languages, using functional and rule-based languages as examples. It also relates these techniques to the practical problems of implementation of languages and algorithms on a von Neumann machine. There are several significant programming projects, programmed in a dialect of the LISP language. http://www.cs.berkeley.edu

Customized version of http://www.thingiverse.com/thing:58731 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=58731

We define a new quasiregular mapping T in three dimensions that generalizes the tangent function on the complex plane and shares a number of its geometric properties. We investigate the dynamics of the family \lambda T for \lambda>0, establishing results analogous to those of Devaney and Keen for the meromorphic family \lambda tan z, \lambda>0, although the methods used are necessarily original.

The discrete ordinates method is widely used to solve the Boltzmann transport equation for neutral particle transport for many engineering applications. Source iteration is used to solve the discrete ordinates system of equations, but can be slow to converge in highly scattering problems. Synthetic acceleration techniques have been developed to address this shortcoming; however, recent research has shown synthetic acceleration to lose effectiveness or diverge for certain problems. LTC Wager introduced an alternative to source iteration and demonstrated it in slab geometry. Here the method is further developed, enhancing efficiency in various ways, and demonstrated in XY-geometry as well as slab geometry. It is shown to be efficient even for those problems for which diffusion-synthetic and transport-synthetic accelerations fail or are ineffective. The method has significant advantages for massively-parallel implementations.

In this paper, we introduce an iterative linearization scheme that allows to approximate the weak solution of the $p$-Poisson problem \begin{align*} -\operatorname{div}(|\nabla u|^{p-2}\nabla u) &= f\quad\text{in }\Omega, u&= 0\quad\text{on}\partial\Omega \end{align*} for $1 < p \leq 2$. The algorithm can be interpreted as a relaxed Ka\v{c}anov iteration. We prove that the algorithm converges at least with an algebraic rate.

Perma.cc archive of https://www.dictionary.com/browse/iteration created on 2022-03-24 06:39:44.131329+00:00.

Perma.cc archive of https://www.dictionary.com/browse/iteration created on 2022-03-24 06:39:44.131329+00:00.

Inscription on the First Official Version of the Mary Phagan History Sign-Post (1994-1995) Culture wars in the middle years of 1990s surrounding the historic Marietta Cemetery, located at the North-West outskirts of greater Atlanta, Georgia.   Image: The little known lettering at the top image--compiled by the long-time journalist and hometown city of Marietta historian, Bill Kinney--is variation part one of two dramatically different renditions of wording formulations, regarding the highly visible posted marker, about the historical significance of rape-murder victim, Mary Anne Phagan (1899-1913).   Backstory   The sign-post was first placed in the historic burial grounds of the Marietta cemetery, in November 1994 or thereabouts, in proximity terms, only several paces away from Mary Phagan's grave and the Phagan family plot. Her final resting place has been a tourist attraction ever since she was interred there on Tuesday, April 29th, 1913. Now more than ever, people are interested in the case, because the Leo Frank case is being re-opened and examined.   The lettering for the Mary Phagan sign post (1994-1995).   The first sign was either destroyed in 1995 or thereafter, though rumor has it that initial sign-post is presently housed in the Marietta History Museum. Further research will need to be done to determine what happened to this controversial first sign-post, one which was intentionally suppressed by the leadership and prominent activists of the local Jewish community.   Transcribed   Mary Phagan Celebrated in song as "Little Mary Phagan" after her murder on Confederate Memorial Day, 1913, in Atlanta. Grave marked by CSA veterans in 1915. Tribute by Tom Watson set 1933. Leo Frank, sentenced to hang, granted clemency before lynching August 17, 1915. His 1986 pardon is based on State's failure to protect him/apprehend killers, not Frank's innocence.   [End of Transcription]   How the Cultural Conflict Unfolded: November, 1995, Marietta, Ethnic Warfare Behind Closed Doors   Jewish members of city council perfidiously decided in an unlawfully closed and highly secretive session, without any public notification to the overwhelmingly Gentile populace, neither before or after the event--had, clandestinely organizing themselves in a quasi-official capacity to alter the Mary Phagan sign post. Their agreed upon furtive mandate was removing mention that the State of Georgia does not recognize Leo Frank to be innocent, and several other notable elements, such as who (Confederate Veterans) placed the tombstone on the formerly paupers grave on June 25th, 1915, and references to the 1933 marble slab above the buried casket, with a touching memorial dedication written by the then-deceased U.S. Congressman for Georgia, Thomas Edward Watson (September 5, 1856 – September 26, 1922).   The Wishful Thinking of Leo Frank's Innocence   The State of Georgia regards Leo Frank as duly convicted on August 25th and 26th of 1913 of the Mary Anne Phagan rape-murder on Saturday, which occurred on April 26, 1913. Numerous appeals to the State and Federal laws determined with majority decisions in 1914 and 1915, that Leo Frank had a fair trial. This is despite the fact some 70 years thereafter the Jewish community pressed for a re-evaluation of the case by the Georgia Pardon's tribunal, between 1982-1986. He was issued a posthumously pardoned March 11, 1986, in a quasi-legalistic ruling which was unlawful according to former Georgian Judge Randall Evans.   Leo Frank is not absolved of his act of homicide   The State of Georgia's pardon's tribunal stated on March 11th, 1986, they were not addressing the subject of Leo Frank's guilt or innocence, thereby leaving the verdict of his 1913 conviction undisturbed. In the eyes of the law, Leo Frank is still guilty as of 2020, and this has left the Jewish community quietly, but determinedly incensed. Jewish activists continue to agitate on Leo Frank's behalf seeking his full absolution of the Phagan sexual assault and slaying.   Appendix   Judge Randall Evans, pointed out the unlawful nature of Leo Frank's posthumous pardon. Not only did the Georgia Board of Pardons and Paroles communicate in its official capacity that Leo Frank was not absolved for the murder of Mary Phagan, but a prominent judged informed the public that the pardon itself was illegal.   The Leo Frank posthumous pardon ordered by the Georgia Board of Pardons and Paroles was de jure unconstitutional, but de facto pseudo-official.   Topics: Mary Phagan murder, Mary Phagan, Leo Frank, Atlanta, Randall Evans, Joe Boone   Letter from retired judge Randall Evans, Jr. to the Honorable Joe Boone stating that the posthumous pardon of Leo Frank for the murder of Mary Phagan was flawed and not legal.   RANDALL EVANS, JR. Judge (Retired)   COURT OF APPEALS OF THE STATE OF GEORGIA ATLANTA March 18, 1986   Honorable Joe Boone Box 265 Toomsboro, Georgia   Dear Joe,   Thank you very much for the book – I am sure I will enjoy it.   I was not surprised at the Leo Frank pardon. The Jewish Community, aided by Joe Frank Harris and that [sic] Atlanta Newspapers, conducted their inquiry by stealth. A pardon to a dead man has no value whatever and is as illegal as anything ever could be.   A pardon must be applied for by the individual and it is personal – just as a divorce is personal. After death, a divorce (and pardon) can not be granted.   With assurances of personal esteem, I am   Sincerely,   [Signature]   Randall Evans, Jr.

This is a Serpinski Pyramid with 4 Triangle faces. Each face adds an iteration of the Serpinski Triangle fractal. Face 1 = solid Face 2 = 3 solid triangles, 1 hole triangle Face 3 = 9 solid triangles, 4 hole triangles Face 4 = 27 solid triangles, 13 hole triangles Added Optional "SerpinskiPyramidConnectors01.stl" file to help glue these together to continue the iterations. (Optional) To iterate by stacking these: 1. Print 4 Pyramids 2. Print 6 connectors 3. Stack Pyramids and glue on connectors as pictured to brace them in place. 4. Do steps 1 to 3 x 4 for each new iteration and stack as large as you dare. Warning: Scaling this item can result in very weak joints between the internal triangles. I recommend printing at 100% scale. I did manage to print a 50% scale version but needed some super glue to reinforce the triangle bonds.

Holder to zip tie onto the back of the WOWs to keep cufflators from doing nosedives as well as hold the iphones we use at our facility and some random other stuff. Needs supports to print, but otherwise should be easy to print. The 1 series I made was specific to the Metro Access point WOW/COW, though it may work for other carts, but there is new designs on the way for that! DISS threaded for O2 Christmas trees. Zip ties should be the only extra thing you need to complete, and i personally strap them to the back of the cart, but in theory it could be put on the front though the nubs are spaced specifically to fit in the screw holes for the aforementioned cart brand.

Audio files associated with the thesis titled  Our Land is Our Life: Learning from Chinook "King" Salmon  by Sarah Mason

Audio files associated with the thesis titled  Our Land is Our Life: Learning from Chinook "King" Salmon  by Sarah Mason

You'll need an Intel Mac to run it.

You'll need an Intel Mac to run it.

Hello Everyone I had a try at designing a car body, i called it the Asp after the Reptile because of the Fierce Reputation it has in the history. Please leave your thoughts in the comments down below.

Using For loops to iterate through iterable values. Unpacking usiing mutliple iterables. Source: https://www.youtube.com/watch?v=Xwa-P-dGtwE Uploader: Christopher Long

A standard problem in scientific computation is the optimization of a smooth (at least twice differentiable) function, possibly subject to smooth constraints. Here, optimization means finding the maximum or minimum value of the function in some region, or perhaps its stationary points. The algorithm presented in this paper solves this problem for regions which are rectangular in form. The method used is a version of interval iteration which finds one or all of the critical points of the function in the given region (the point or points at which its gradient vector vanishes), or just the critical points at which the function has its maximum or minimum values. The required values of the gradient vector and Hessian matrix of the function are obtained by automatic differentiation, which does not involve symbolic differentiation or numerical approximation of the derivatives of the function being investigated. Unlike algorithms which sample function values only at a discrete set of points, the ones given here use interval computation to furnish guaranteed bounds for all quantities of interest over the required subregions of the initial region. The results given by these optimization algorithms are thus self-validating. The algorithms presented here have been programmed using standard implementations of automatic differentiation and interval computation. Numerical examples are given to illustrate the effectiveness of this approach to the type of optimization problem considered.

A theory of interval iteration, based on a few simple assumptions, is given for the fixed point problem for operators in partially ordered topological spaces. A comparison of interval with ordinary iteration is made which shows that their properties are converse in a certain sense with respect to existence or nonexistence of fixed points. The theory of interval iteration is shown to hold without modification if the computation is restricted to a finite set of points, as in actual practice. In this latter case interval iteration is show to converge or diverge in a finite number of steps, for which an upper bound is given. By the introduction of a suitable iteration operator, the method of interval iteration is extended to the problem of solution of equations in linear spaces. (Author)

A theory of interval iteration, based on a few simple assumptions, is given for the fixed point problem for operators in partially ordered topological spaces. A comparison of interval with ordinary iteration is made which shows that their properties are converse in a certain sense with respect to existence or nonexistence of fixed points. The theory of interval iteration is shown to hold without modification if the computation is restricted to a finite set of points, as in actual practice. In this latter case interval iteration is show to converge or diverge in a finite number of steps, for which an upper bound is given. By the introduction of a suitable iteration operator, the method of interval iteration is extended to the problem of solution of equations in linear spaces. (Author)

Solving Markov Decision Processes (MDPs) is a recurrent task in engineering. Even though it is known that solutions for minimizing the infinite horizon expected reward can be found in polynomial time using Linear Programming techniques, iterative methods like the Policy Iteration algorithm (PI) remain usually the most efficient in practice. This method is guaranteed to converge in a finite number of steps. Unfortunately, it is known that it may require an exponential number of steps in the size of the problem to converge. On the other hand, many open questions remain considering the actual worst case complexity. In this work, we provide the first improvement over the fifteen years old upper bound from Mansour & Singh (1999) by showing that PI requires at most k/(k-1)*k^n/n + o(k^n/n) iterations to converge, where n is the number of states of the MDP and k is the maximum number of actions per state. Perhaps more importantly, we also show that this bound is optimal for an important relaxation of the problem.

In this article and in its sequel we propose the study of certain discretizations of geometric evolution equations as an approach to the study of the existence problem of some elliptic partial differential equations of a geometric nature as well as a means to obtain interesting dynamics on certain infinite-dimensional spaces. We illustrate the fruitfulness of this approach in the context of the Ricci flow, as well as another flow, in Kahler geometry. We introduce and study dynamical systems related to the Ricci operator on the space of Kahler metrics that arise as discretizations of these flows. We pose some problems regarding their dynamics. We point out a number of applications to well-studied objects in Kahler and conformal geometry such as constant scalar curvature metrics, Kahler-Ricci solitons, Nadel-type multiplier ideal sheaves, balanced metrics, the Moser-Trudinger-Onofri inequality, energy functionals and the geometry and structure of the space of Kahler metrics. E.g., we obtain a new sharp inequality strengthening the classical Moser-Trudinger-Onofri inequality on the two-sphere.

This study is an extension of work done by Charles Ashbacher. Iteration results have been re-defined in terms of invariants and loops. Further empirical studies and analysis of results have helped throw light on a few intriguing questions.

We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information leakage; and we propose a program algebra for source-level reasoning about such programs, in particular as a means of establishing that an "implementation" program leaks no more than its "specification" program. This joins two themes: we extend our earlier work, having iteration but only qualitative, by making it quantitative; and we extend our earlier quantitative work by including iteration. We advocate stepwise refinement and source-level program algebra, both as conceptual reasoning tools and as targets for automated assistance. A selection of algebraic laws is given to support this view in the case of quantitative noninterference; and it is demonstrated on a simple iterated password-guessing attack.

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of hyperbolic cocycles over a rotation. We present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori.

The classical division algorithm for polynomials requires $O(n^2)$ operations for inputs of size $n$. Using reversal technique and Newton iteration, it can be improved to $O({M}(n))$, where ${M}$ is a multiplication time. But the method requires that the degree of the modulo, $x^l$, should be the power of 2. If $l$ is not a power of 2 and $f(0)=1$, Gathen and Gerhard suggest to compute the inverse,$f^{-1}$, modulo $x^{\lceil l/2^r\rceil}, x^{\lceil l/2^{r-1}\rceil},..., x^{\lceil l/2\rceil}, x^l$, separately. But they did not specify the iterative step. In this note, we show that the original Newton iteration formula can be directly used to compute $f^{-1}\,{mod}\,x^{l}$ without any additional cost, when $l$ is not a power of 2.

Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the $\ell$-wave solutions of the Schr\"{o}dinger equation with the Manning-Rosen potential. The equation of energy eigenvalues equation and the corresponding wavefunctions have been obtained explicitly. Three different Pekeris-type approximation schemes have been used to deal with the centrifugal term. To show the accuracy of our results, we have calculated the eigenvalues numerically for arbitrary quantum numbers $n$ and $\ell$ for some diatomic molecules (HCl, CH, LiH and CO). It is found that the results are in good agreement with other results found in the literature. A straightforward extension to the s-wave case and Hulth$\acute{e}$n potential case are also presented.

In this paper we apply methods of proof mining to obtain a uniform effective rate of asymptotic regularity for the Mann iteration associated to $\kappa$-strict pseudo-contractions on convex subsets of Hilbert spaces.

This paper studies approximate policy iteration (API) methods which use least-squares Bellman error minimization for policy evaluation. We address several of its enhancements, namely, Bellman error minimization using instrumental variables, least-squares projected Bellman error minimization, and projected Bellman error minimization using instrumental variables. We prove that for a general discrete-time stochastic control problem, Bellman error minimization using instrumental variables is equivalent to both variants of projected Bellman error minimization. An alternative to these API methods is direct policy search based on knowledge gradient. The practical performance of these three approximate dynamic programming methods are then investigated in the context of an application in energy storage, integrated with an intermittent wind energy supply to fully serve a stochastic time-varying electricity demand. We create a library of test problems using real-world data and apply value iteration to find their optimal policies. These benchmarks are then used to compare the developed policies. Our analysis indicates that API with instrumental variables Bellman error minimization prominently outperforms API with least-squares Bellman error minimization. However, these approaches underperform our direct policy search implementation.

In this paper, for an $\lambda$-strict pseudocontraction $T$, we prove strong convergence of the modified Mann's iteration defined by $$x_{n+1}=\beta_{n}u+\gamma_nx_n+(1-\beta_{n}-\gamma_n)[\alpha_{n}Tx_n+(1-\alpha_{n})x_n],$$ where $\{\alpha_{n}\}$, $ \{\beta_{n}\}$ and $\{\gamma_n\}$ in $(0,1)$ satisfy: (i) $0 \leq \alpha_{n}\leq \frac{\lambda}{K^2}$ with $\liminf\limits_{n\to\infty}\alpha_n(\lambda-K^2\alpha_n)> 0$; (ii) $\lim\limits_{n\to\infty}\beta_n= 0$ and $\sum\limits_{n=1}^\infty\beta_n=\infty$; (iii) $\limsup\limits_{n\to\infty}\gamma_n

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any given fixed rank. However, the SVD is also known to be very costly to compute. Among the different approaches in the literature for computing low-rank approximations, randomized algorithms have attracted researchers' recent attention due to their surprising reliability and computational efficiency in different application areas. Typically, such algorithms are shown to compute with very high probability low-rank approximations that are within a constant factor from optimal, and are known to perform even better in many practical situations. In this paper, we present a novel error analysis that considers randomized algorithms within the subspace iteration framework and show with very high probability that highly accurate low-rank approximations as well as singular values can indeed be computed quickly for matrices with rapidly decaying singular values. Such matrices appear frequently in diverse application areas such as data analysis, fast structured matrix computations and fast direct methods for large sparse linear systems of equations and are the driving motivation for randomized methods. Furthermore, we show that the low-rank approximations computed by these randomized algorithms are actually rank-revealing approximations, and the special case of a rank-1 approximation can also be used to correctly estimate matrix 2-norms with very high probability. Our numerical experiments are in full support of our conclusions.

Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions which focus on policy representation using classifiers and address policy learning as a supervised learning problem. This paper proposes variants of an improved policy iteration scheme which addresses the core sampling problem in evaluating a policy through simulation as a multi-armed bandit machine. The resulting algorithm offers comparable performance to the previous algorithm achieved, however, with significantly less computational effort. An order of magnitude improvement is demonstrated experimentally in two standard reinforcement learning domains: inverted pendulum and mountain-car.

In this paper, a new kind of multigrid method is proposed for the ground state solution of Bose-Einstein condensates based on Newton iteration method. Instead of treating eigenvalue $\lambda$ and eigenvector $u$ respectively, we regard the eigenpair $(\lambda, u)$ as one element in the composite space $\R \times H_0^1(\Omega)$ and then Newton iteration method is adopted for the nonlinear problem. Thus in this multigrid scheme, we only need to solve a linear discrete boundary value problem in every refined space, which can improve the overall efficiency for the simulation of Bose-Einstein condensations.

This paper formulates and presents a solution to the new problem of budgeted semantic video segmentation. Given a video, the goal is to accurately assign a semantic class label to every pixel in the video within a specified time budget. Typical approaches to such labeling problems, such as Conditional Random Fields (CRFs), focus on maximizing accuracy but do not provide a principled method for satisfying a time budget. For video data, the time required by CRF and related methods is often dominated by the time to compute low-level descriptors of supervoxels across the video. Our key contribution is the new budgeted inference framework for CRF models that intelligently selects the most useful subsets of descriptors to run on subsets of supervoxels within the time budget. The objective is to maintain an accuracy as close as possible to the CRF model with no time bound, while remaining within the time budget. Our second contribution is the algorithm for learning a policy for the sparse selection of supervoxels and their descriptors for budgeted CRF inference. This learning algorithm is derived by casting our problem in the framework of Markov Decision Processes, and then instantiating a state-of-the-art policy learning algorithm known as Classification-Based Approximate Policy Iteration. Our experiments on multiple video datasets show that our learning approach and framework is able to significantly reduce computation time, and maintain competitive accuracy under varying budgets.

Let $K$ be an algebraically closed field that is complete with respect to a non-Archimedean absolute value, and let $\varphi\in K(z)$ have degree $d\geq 2$. We characterize maps for which the minimal resultant of an iterate $\varphi^n$ is given by a simple formula in terms of $d$, $n$, and the minimal resultant of $\varphi$. We show that such maps are precisely those with reduction outside of an indeterminacy locus $I(d)$ and which also have semi-stable reduction for every iterate $\varphi^n$. We give two equivalent ways of describing such maps, one measure theoretic and the other in terms of the moduli space $\mathcal{M}_d$ of degree $d$ rational maps. As an application, we are able to give an explicit formula for the minimal value of the diagonal Arakelov-Green's function of a map satisfying the conditions of the main theorem. We illustrate our results with some explicit calculations in the case of the Latt\`es maps.

We compute uniform rates of metastability for the Ishikawa iteration of a Lipschitz pseudo-contractive self-mapping of a compact convex subset of a Hilbert space. This extraction is an instance of the proof mining program that aims to apply tools from mathematical logic in order to extract the hidden quantitative content of mathematical proofs. We prove our main result by applying methods developed by Kohlenbach, the first author and Nicolae for obtaining quantitative versions of strong convergence results for generalized Fej\'er monotone sequences in compact subsets of metric spaces.

In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge; Brouwer disagrees on both counts. I will compare Parsons' argument with Brouwer's and defend the latter. I will not argue that Parsons is wrong once his own conception of intuition is granted, as I do not think that that is the case. But I will try to make two points: (1) Using elements from Husserl and from Brouwer, Brouwer's claims can be justified in more detail than he has done; (2) There are certain elements in Parsons' discussion that, when developed further, would lead to Brouwer's notion thus analysed, or at least something relevantly similar to it. (This version contains a postscript of May, 2015.)

The Berry Center was started in 2011 to continue the agricultural work of John Berry, Sr. and his sons Wendell Berry and John Berry, Jr. John Berry, Sr. was a staunch advocate for small farmers and land conserving economies. His sons took up his work and have continued it. The Berry Center has now taken it up, and is focused on issues confronting small farming families in Kentucky and around the country. We are asking and trying to answer two of the most essential questions of our time; “What will it take for farmers to be able to afford to farm well?” and “How do we become a culture that will support good land use?” These questions are nowhere in the public discourse and yet the answers will go a long way in solving the most serious issues we now face. Our focus may shift because of need, but it will not move from what we believe to be the central issue of our time: the need for a healthy and sustainable agriculture in this country.