Multi-variable translation equation which arises from homothety

In many regular cases, there exists a (properly defined) limit of iterations of a function in several real variables, and this limit satisfies the functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a vector. This is a special case of a well-known translation equation. In this paper we present a complete solution to this functional equation in case f is a continuous function on a single point compactification of a 2-dimensional real vector space. It appears that, up to conjugation by a homogeneous continuous function, there are exactly four solutions. Further, in a 1-dimensional case we present a solution with no regularity assumptions on f.Comment: 15 page

The DSF Quorum Sensing System Controls the Positive Influence of Stenotrophomonas maltophilia on Plants

none7siopenAlavi P.; Muller H.; Cardinale M.; Zachow C.; Sanchez M.B.; Martinez J.L.; Berg G.Alavi, P.; Muller, H.; Cardinale, M.; Zachow, C.; Sanchez, M. B.; Martinez, J. L.; Berg, G

Add a little more: a new mannerism in recent Flemish architecture

This article discusses, mainly with reference to recent work by the architecture office De Vylder Vinck Taillieu, new tendencies in Belgian architecture that use form in architectural design in a way that may be called Mannerist. The term is systematically developed and explained, and then introduced in a critical discussion of the newly built community center L-Berg and the House Huik

On the theory of convolution equations of the third kind

AbstractThe autoconvolution equation of the third kind with coefficient of general power type is dealt with by the method of weighted norms developed for equations with coefficients of linear and integer power type in recent joint work of the author with L. Berg, J. Janno, and B. Hofmann. For this equation two existence theorems and a uniqueness theorem are proved. Further, as an auxiliary equation a linear singular integral equation of Abel is treated anew and the existence of solutions to a related class of linear Volterra equations of the third kind is derived

The projective translation equation and rational plane flows. I

Let X=(x,y). A plane flow is a function F(X,t): R^2*R->R^2 such that F(F(X,s),t)=F(X,s+t) for (almost) all real numbers x,y,s,t (the function F might not be well-defined for certain x,y,t). In this paper we investigate rational plane flows which are of the form F(X,t)=f(Xt)/t; here f is a pair of rational functions in 2 real variables. These may be called projective flows, and for a description of such flows only the knowledge of Cremona group in dimension 1 is needed. Thus, the aim of this work is to completely describe over R all rational solutions of the two dimensional translation equation (1-z)f(X)=f(f(Xz)(1-z)/z). We show that, up to conjugation with a 1-homogenic birational plane transformation (1-BIR), all solutions are as follows: a zero flow, two singular flows, an identity flow, and one non-singular flow for each non-negative integer N, called the level of the flow. The case N=0 stands apart, while the case N=1 has special features as well. Conjugation of these canonical solutions with 1-BIR produce a variety of flows with different properties and invariants, depending on the level and on the conjugation itself. We explore many more features of these flows; for example, there are 1, 4, and 2 essentially different symmetric flows in cases N=0, N=1, and N>=2, respectively. Many more questions will be treated in the second part of this work.Comment: 54 pages, 6 figures. Final version before proof

Solving Visual Madlibs with Multiple Cues

This paper focuses on answering fill-in-the-blank style multiple choice questions from the Visual Madlibs dataset. Previous approaches to Visual Question Answering (VQA) have mainly used generic image features from networks trained on the ImageNet dataset, despite the wide scope of questions. In contrast, our approach employs features derived from networks trained for specialized tasks of scene classification, person activity prediction, and person and object attribute prediction. We also present a method for selecting sub-regions of an image that are relevant for evaluating the appropriateness of a putative answer. Visual features are computed both from the whole image and from local regions, while sentences are mapped to a common space using a simple normalized canonical correlation analysis (CCA) model. Our results show a significant improvement over the previous state of the art, and indicate that answering different question types benefits from examining a variety of image cues and carefully choosing informative image sub-regions

Learning Temporal Transformations From Time-Lapse Videos

Based on life-long observations of physical, chemical, and biologic phenomena in the natural world, humans can often easily picture in their minds what an object will look like in the future. But, what about computers? In this paper, we learn computational models of object transformations from time-lapse videos. In particular, we explore the use of generative models to create depictions of objects at future times. These models explore several different prediction tasks: generating a future state given a single depiction of an object, generating a future state given two depictions of an object at different times, and generating future states recursively in a recurrent framework. We provide both qualitative and quantitative evaluations of the generated results, and also conduct a human evaluation to compare variations of our models.Comment: ECCV201

Singularity results for functional equations driven by linear fractional transformations

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.Comment: 14 pages, Title changed, to appear in Journal of Theoretical Probabilit