Related papers: Effective descent morphisms of filtered preorders
In the setting of message passing software, De Nicola and Hennessy must-preorder defines when a program improves on another one. Since this preorder does not come equipped with a viable proof method, using it requires an alternative…
In a category $\mathcal{C}$ with a proper $(\mathcal{E}, \mathcal{M})$-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow…
The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of…
Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the…
Higher-order mutation has the potential for improving major drawbacks of traditional first-order mutation, such as by simulating more realistic faults or improving test optimization techniques. Despite interest in studying promising…
Linear second order recursive sequences with arbitrary initial conditions are studied. For sequences with the same parameters a ring and a group is attached, and isomorphisms and homomorphisms are established for related parameters. In the…
This paper provides a rigorous derivation for what is known in the literature as the Lie bracket approximation of control-affine systems in a more general and sequential framework for higher-orders. In fact, by using chronological calculus,…
In this paper, we have considered the dense rank for assigning positions to alternatives in weak orders. If we arrange the alternatives in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the alternatives in the…
The architecture of a deep neural network is defined explicitly in terms of the number of layers, the width of each layer and the general network topology. Existing optimisation frameworks neglect this information in favour of implicit…
We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational…
We systematically investigate the functors between sites which induce morphisms of relative toposes. In particualar, we establish a relative version of Diaconescu's theorem, characterizing the relative geometric morphisms towards a relative…
In the 1970s M. Laczkovich posed the following problem: Let $\mathcal{B}_1(X)$ denote the set of Baire class $1$ functions defined on an uncountable Polish space $X$ equipped with the pointwise ordering. \[\text{Characterize the order types…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
In the context of deep learning, many optimization methods use gradient covariance information in order to accelerate the convergence of Stochastic Gradient Descent. In particular, starting with Adagrad, a seemingly endless line of research…
Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function \omega with a linear transformation. This setting includes Group Lasso methods,…
This paper presents a memory efficient, first-order method for low multi-linear rank approximation of high-order, high-dimensional tensors. In our method, we exploit the second-order information of the cost function and the constraints to…
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…