We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a “sequentialized” version of any static kernel. The sequential kernels are efficiently computable for discrete sequences and are...

A sequential-move version of a given normal-form game Γ is an extensive-form game of perfect information in which each player chooses his action after observing the actions of all players who precede him and the payoffs are determined according to the payoff functions in Γ. A normal-form game Γ is sequentially solvable if each of its sequential-move versions has a subgame-perfect equilibrium in...

We prove a multiclass boosting theory for the ResNet architectures which simultaneously creates a new technique for multiclass boosting and provides a new algorithm for ResNet-style architectures. Our proposed training algorithm, BoostResNet, is particularly suitable in non-differentiable architectures. Our method only requires the relatively inexpensive sequential training of T “shallow ResNet...

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

Throughout the early and mid 1990s, there was widespread faith in the compact city model's ability to provide urban sustainability. However, where compact city policies had been implemented, follow-up studies began to show the predicted benefits did not happen as they should be. The article tries to peruse two opposite approaches of "Urban Sprawl" and "Compact City", with an analytical - cri...

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product [X × H × Y ]σ of a topological group H over topological spaces X, Y with a continuous sandwich function σ : Y × X → H. We prove that a simple topological semigroup S is a topological paragroup if one of the following conditions is satisfied: (1) S is completely simple and the maximal subgrou...

This document establishes that the result in "Sequentially Optimal Mechanisms" is robust to a number of extensions. 1. Robustness: Longer Horizon & Alternative Degrees of Transparency We will show that our result is robust in a number of di¤erent directions. The …rst extension considers the possibility that the game lasts arbitrarily long, but …nitely many periods. The next three extensions are...

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...