Module structures and the derived functors of iterated loop functors on unstable modules over the Steenrod algebra

The calculation of the iterated loop functors and their left derived functors on the category of unstable modules over the Steenrod algebra is a non-trivial problem; Singer constructed an explicit and functorial chain complex to calculate these functors. The results of Singer are analysed to give information on the behaviour of these functors with respect to the nilpotent filtration of the category of unstable modules.We show that, if an unstable module M supports an action of an unstable algebra K, then the derived functors of the iterated loop functors applied to M support actions of iterated doubles of K. This allows the finiteness results of Henn on unstable modules which support actions of unstable algebras to be applied to deduce structural results on the derived functors of iterated loops on such modules.     

Robot learning schemes that trade motion accuracy for command simplification

This study was inspired by the human motor control system in its ability to accommodate a wide variety of motions. By contrast, the biologically inspired robot learning controller usually encounters huge learning space problems in many practical applications. A hypothesis for the superiority of the human motor control system is that it may have simplified the motion command at the expense of motion accuracy. This tradeoff provides an insight into how fast and simple control can be achieved when a robot task does not demand high accuracy. Two motion command simplification schemes are proposed in this paper based on the equilibrium-point hypothesis for human motion control. Investigation into the tradeoff between motion accuracy and command simplification reported in this paper was conducted using robot manipulators to generate signatures. Signature generation involves fast handwriting, and handwriting is a human skill acquired via practice. Because humans learn how to sign their names after they learn how to write, in the second learning process, they somehow learn to trade motion accuracy for motion speed and command simplicity, since signatures are simplified forms of original handwriting. Experiments are reported that demonstrate the effectiveness of the proposed schemes.     

MODELING THE MOVEMENTS OF COWBIRDS: APPLICATION TOWARDS MANAGEMENT AT THE LANDSCAPE SCALE

ABSTRACT. Brood parasitism by brown‐headed cowbirds (Molothrus ater) reduces the reproductive success of two endangered bird species at Fort Hood, Texas. A successful management program has focused on trapping cowbirds at feeding locations, grassland areas almost always associated with the presence of cattle. To enhance the efficacy of this effort, we developed an individual‐based model that predicted visitation rates by cowbirds to all potential feeding locations at Fort Hood and the surrounding landscape. Utilizing GRASS‐GIS and SWARM, the model incorporated the spatial arrangement of habitats, daily movements of cattle, and daily movements of cowbirds from their breeding sites to feeding locations. We simulated four types of movements by cow‐birds as they searched for cattle: 1) random walk, 2) direct return to previous locations (i.e., memory), 3) return to previous locations with en route assessment (i.e., memory with limited perception of the current state of the system), and 4) omniscience. Straight‐line distances between breeding and feeding locations for cowbirds that used the memory‐with‐perception rule were similar to independent telemetry results, and total search distances for this movement type approached those of omniscience. Both movement distance measures were inversely related to perception distance. Maps of cowbird visits to feeding areas differed among movement rules but were not strongly affected by the density of breeding cow‐birds. Maps also identified locations where trapping efforts could reduce parasitism within specific areas known to support endangered species. While it seems plausible that cowbirds are able to remember foraging locations and to perceive their surroundings as they travel, additional studies are needed to document their cognitive abilities. By simulating movements of individual cowbirds across a dynamic landscape, model results may help to strengthen ongoing cowbird control efforts.     

An integrable hierarchy including the AKNS hierarchy and its strict version

We present an integrable hierarchy that includes both the AKNS hierarchy and its strict version. We split the loop space g of gl₂ into Lie subalgebras g≥0 and g<0 of all loops with respectively only positive and only strictly negative powers of the loop parameter. We choose a commutative Lie subalgebra C in the whole loop space s of sl₂ and represent it as C = C≥0⊕C<0. We deform the Lie subalgebras C≥0 and C<0 by the respective groups corresponding to g<0 and g≥0. Further, we require that the evolution equations of the deformed generators of C≥0 and C<0 have a Lax form determined by the original splitting. We prove that this system of Lax equations is compatible and that the equations are equivalent to a set of zero-curvature relations for the projections of certain products of generators. We also define suitable loop modules and a set of equations in these modules, called the linearization of the system, from which the Lax equations of the hierarchy can be obtained. We give a useful characterization of special elements occurring in the linearization, the so-called wave matrices. We propose a way to construct a rather wide class of solutions of the combined AKNS hierarchy.     

Incidence properties of cosets in loops

We study incidence properties among cosets of infinite loops, with emphasis on well‐structured varieties such as antiautomorphic loops and Bol loops. While cosets in groups are either disjoint or identical, we find that the incidence structure in general loops can be much richer. Every symmetric design, for example, can be realized as a canonical collection of cosets of a infinite loop. We show that in the variety of antiautomorphic loops the poset formed by set inclusion among intersections of left cosets is isomorphic to that formed by right cosets. We present an algorithm that, given a infinite Bol loop S, can in some cases determine whether |S| divides |Q| for all infinite Bol loops Q with S?Q, and even whether there is a selection of left cosets of S that partitions Q. This method results in a positive confirmation of Lagrange's Theorem for Bol loops for a few new cases of subloops. Finally, we show that in a left automorphic Moufang loop Q (in particular, in a commutative Moufang loop Q), two left cosets of S?Qare either disjoint or they intersect in a set whose cardinality equals that of some subloop of S.     

Collaborative distributed decision making for large scale disaster relief operations: Drawing analogies from robust natural systems

One of the most ignored, but urgent and vital challenges confronting society today is the vulnerability of urban areas to extreme events. Current organization of response systems, predominantly based on a command and control model, limits their effectiveness and efficiency. Particularly, in decision‐making processes where a large number of actors may be involved. In this article, a new distributed collaborative decision‐making model is proposed to overcome command and control limitations encountered in stressful, hostile, chaotic, and large‐scale settings. This model was derived by borrowing concepts from the collective decision making of honeybees foraging, a successful process in solving complex tasks within complex settings. The model introduced in this article was evaluated through differential equations, i.e., continuous analysis, and difference equations, i.e., discrete analysis. The most important result found is that the best available option in any large‐scale decision‐making problem can be configured as an attractor, in a distributed and timely manner. We suggest that the proposed model has the potential to facilitate decision‐making processes in large‐scale settings. © 2005 Wiley Periodicals, Inc. Complexity 11:28–38, 2005     

An improved efficiency of fuzzy logic control of PMBLDC for PV pumping system

This paper presents an analysis by which the dynamic performances of a permanent magnet brushless DC (PMBLDC) motor is controlled through a hysteresis current loop and an outer speed loop with different controllers. The dynamics of the photovoltaic pumping drive system with (PI) and a fuzzy logic (FL) speed controllers are presented. In order to optimize the overall system efficiency, a maximum power point tracker is also used. Simulation is carried out by formatting the mathematical model for photovoltaic source, MPPT, motor and pump load. The results for such complicated and nonlinear system, with FL speed controller show improvement in transient response of PMBLDC drive over conventional PI. The effectiveness of the FL controller is also demonstrated.     

Global Weyl modules for the twisted loop algebra

We define global Weyl modules for twisted loop algebras and analyze their highest weight spaces, which are in fact isomorphic to Laurent polynomial rings in finitely many variables. We are able to show that the global Weyl module is a free module of finite rank over these rings. Furthermore we prove, that there exist injective maps from the global Weyl modules for twisted loop algebras into a direct sum of global Weyl modules for untwisted loop algebras. Relations between local Weyl modules for twisted and untwisted generalized current algebras are known; we provide for the first time a relation on global Weyl modules.     

Optimal System of Loops on an Orientable Surface

Every compact orientable boundaryless surface M can be cut along simple loops with a common point v₀, pairwise disjoint except at v₀, so that the resulting surface is a topological disk; such a set of loops is called a {\it system of loops} for M. The resulting disk may be viewed as a polygon in which the sides are pairwise identified on the surface; it is called a polygonal schema. Assuming that M is a combinatorial surface, and that each edge has a given length, we are interested in a shortest (or optimal) system of loops homotopic to a given one, drawn on the vertex-edge graph of M. We prove that each loop of such an optimal system is a shortest loop among all simple loops in its homotopy class. We give an algorithm to build such a system, which has polynomial running time if the lengths of the edges are uniform. As a byproduct, we get an algorithm with the same running time to compute a shortest simple loop homotopic to a given simple loop.     

Well-posedness results and asymptotic behaviour for a phase transition model taking into account microscopic accelerations

We obtain an existence and uniqueness result to Frémond's phase transition model which take into account microscopic movements and accelerations. Moreover, the irreversible evolution of the phase variable is considered. Next, we perform an asymptotic analysis on the solution to the above problem, as the power of the microscopic acceleration forces goes to zero.     

Towards Riccati-Feedback Control of Complex Flows with Moving Interfaces

Problems featuring moving interfaces appear in many applications. They can model solidification and melting of pure materials, crystal growth and other multi-phase problems. The control of the moving interface enables to, for example, influence production processes and, thus, the product material quality. We consider the two-phase Stefan problem that models a solid and a liquid phase separated by the moving interface. In the liquid phase, the heat distribution is characterized by a convection-diffusion equation. The fluid flow in the liquid phase is described by the Navier–Stokes equations which introduces a differential algebraic structure to the system. The interface movement is coupled with the temperature through the Stefan condition, which adds additional algebraic constraints. Our formulation uses a sharp interface representation and we define a quadratic tracking-type cost functional as a target of a control input. We compute an open loop optimal control for the Stefan problem using an adjoint system. For a feedback representation, we linearize the system about the trajectory defined by the open loop control. This results in a linear-quadratic regulator problem, for which we formulate the differential Riccati equation with time varying coefficients. This Riccati equation defines the corresponding feedback gain. Further, we present the feedback formulation that takes into account the structure and the differential algebraic components of the problem. Also, we discuss how the complexities that come, for example, with mesh movements, can be handled in a feedback setting. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust Control of Robots by Stochastic Optimisation Techniques

In optimal control of robots, engineering practice is to calculate off‐line an optimal open‐loop control, based on nominal values of the model parameters. Due to the deviation between the nominal model parameters and the possible realisations of the model parameters, the performance of the system usually does not correspond to the chosen open‐loop control. Hence, expensive on‐line control corrections are necessary to improve system performance. By incorporating available a priori and statistical information about the unknown model parameters into the control process, these expenses are reduced to a large extent.     

On the Bol Loops

In the present paper, the Bol loops and related groups are studied. We suggest a universal way to construct a Bol loop and find criteria for simplicity and finiteness of such loops.     

Stochastic vs deterministic programming in water management: the value of flexibility

In the paper we develop a two stage scenario-based stochastic programming model for water management in the Indus Basin Irrigation System (IBIS). We present a comparison between the deterministic and scenario-based stochastic programming model. Our model takes stochastic inputs on hydrologic data i.e. inflow and rainfall. We divide the basin into three rainfall zones which overlap on 44 canal commands. Data on crop characteristics are taken on canal command levels. We then use ten-daily and monthly time intervals to analyze the policies. This system has two major reservoirs and a complex network of rivers, canal head works, canals, sub canals and distributaries. All the decisions on hydrologic aspects are governed by irrigation and agricultural development policies. Storage levels are maintained within the minimum and maximum bounds for every time interval according to a power generation policy. The objective function is to maximize the expected revenue from crops production. We discuss the flexibility of two stochastic optimization models with varying time horizon.     

A model structure approach to the finitistic dimension conjectures

We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal {X}$‐dimension, for certain classes of modules $\mathcal {X}$. As an application we give a model structure approach to the finitistic dimension conjectures and present a new conceptual framework in which these conjectures can be studied.     

Small loop spaces

The importance of small loops in the covering space theory was pointed out by Brodskiy, Dydak, Labuz, and Mitra in [2] and [3]. A small loop is a loop which is homotopic to a loop contained in an arbitrarily small neighborhood of its base point and a small loop space is a topological space in which every loop is small. Small loops are the strongest obstruction to semi-locally simply connectedness. We construct a small loop space using the Harmonic Archipelago. Furthermore, we define the small loop group of a space and study its impact on covering spaces, in particular its contribution to the fundamental group of the universal covering space.     

Admissible Orders of Jordan Loops

A commutative loop is Jordan if it satisfies the identity x²(yx) = (x²y)x. Using an amalgam construction and its generalizations, we prove that a nonassociative Jordan loop of order n exists if and only if n≧ 6 and n≠ 9. We also consider whether powers of elements in Jordan loops are well‐defined, and we construct an infinite family of finite simple nonassociative Jordan loops. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 103–118, 2009     

Simple Bol Loops

In this article we investigate the Bol loops and connected with them groups. We prove an analog of the Doro's theorem for Moufang loops and find a criterion for simplicity of Bol loops. One of the main results obtained is the following: If the right multiplication group of a connected finite Bol loop S is a simple group, then S is a Moufang loop.     

A GPSS/H model for a hypothetical flexible manufacturing system

A GPSS/H model is presented for a hypothetical flexible manufacturing system. The FMS consists of six machines composed of three machine types, manufactures three types of parts, and uses automatic guided vehicles (AGVs) to transport inprocess parts between appropriate machines and wait spaces in the system. Three logical modules have been designed for the model, with copies of these modules then being appropriately distributed and interfaced throughout the model and tailored to achieve overall representation of the specific FMS. The same technique can be used by others to build analogous or extended GPSS/H models for other specific FMSs in which AGVs are used as transporters. Simulations can then be performed with such models to research FMS design and control alternatives.     

Diffusion of Loops

We study a lattice model that is closely related to the Ising model and can be regarded as describing diffusion of loops in two dimensions. The time development is given by a transfer matrix for a random surface model on a three-dimensional lattice. The transfer matrix is indexed by loops and is invariant under a group of motions in the loop space. The eigenvalues of the transfer matrix are calculated in terms of the partition function and the correlation functions of the Ising model.