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Rerankers, typically cross-encoders, are computationally intensive but are frequently used because they are widely assumed to outperform cheaper initial IR systems. We challenge this assumption by measuring reranker performance for full…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
This work investigates preserving and reversing unimodality and convexity properties for sequences under transformations defined by sign-regular kernels. It is shown that these transformations only preserve these properties if the kernels…
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
Termination property of functions is an important issue in computability theory. In this paper, we show that repeated iterations of a function can induce an order amongst the elements of its domain set. Hasse diagram of the poset, thus…
In arXiv:2204.03190, we proposed a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. But the method is quite redundant as it does not utilize the results of lower rank cases when…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Inspired by non-Hermitian systems, we study reflection and transmission in a stack of thin films composed by the repetition of a bipartite unit cell. We aim for controlled reflection and transmission using lossless and lossy materials in…
We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We propose a novel approach to stream definition and manipulation. Our solution is based on two key ideas. Regular corecursion, which avoids non termination by detecting cyclic calls, is enhanced, by allowing in equations defining streams…
We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also be applied to resolve open problems in extremal and…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…
Transformers process tokens in parallel but are temporally shallow: at position $t$, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer…
Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)]…
The work presented in this thesis seeks to improve programmer productivity in the following ways: - by reducing the amount of code that has to be written to construct an application; - by increasing the reliability of the code written; and…
This note considers the notion of divergence-preserving branching bisimilarity. It briefly surveys results pertaining to the notion that have been obtained in the past one-and-a-half decade, discusses its role in the study of expressiveness…