# Amin FarjudianUniversity of Nottingham Ningbo China | Ningbo · School of Computer Science

Amin Farjudian

PhD in Computer Science, BSc in Pure Maths

## About

39

Publications

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94

Citations

Introduction

Additional affiliations

October 2017 - present

May 2015 - September 2017

October 2009 - May 2015

## Publications

Publications (39)

Robustness is a property of system analyses, namely monotonic maps from the complete lattice of subsets of a (system's state) space to the two-point lattice. The definition of robustness requires the space to be a metric space. Robust analyses cannot discriminate between a subset of the metric space and its closure, therefore one can restrict to th...

Knowledge representation is the cornerstone of constructing a GKG. The existing representations of spatial and computational relations in GKGs, however, are inadequate. In this paper, we use DE-9IM to represent spatial topological relations. To represent computational relations, we use typed lambda calculus via its implementation in the functional...

We present a domain-theoretic framework for validated robustness analysis of neural networks. We first analyze the global robustness of a general class of networks. Then, using the fact that Edalat's domain-theoretic L-derivative coincides with Clarke's generalized gradient, we extend our framework for attack-agnostic local robustness analysis. Our...

Contribution: Using threshold concepts as the framework for curriculum design, a project on neural network methods for solving differential equations is presented, with a rich set of transformative concepts from mathematics and computer science. Projects of this kind complement a typical curriculum with expertise that is crucial for critique and fu...

A domain-theoretic method for solving initial value problems (IVPs) is presented, together with proofs of soundness, completeness, and some results on the algebraic complexity of the method. While the common fixed-precision interval arithmetic methods are restricted by the precision of the underlying machine architecture , domain-theoretic methods...

Software is increasingly embedded in a variety of physical contexts. This imposes new requirements on tools that support the design and analysis of systems. For instance, modeling embedded and cyber-physical systems needs to blend discrete mathematics, which is suitable for modeling digital components, with continuous mathematics, used for modeling...

Software is increasingly embedded in a variety of physical contexts. This imposes new requirements on tools that support the design and analysis of systems. For instance, modeling embedded and cyber-physical systems needs to blend discrete mathematics, which is suitable for modeling digital components, with continuous mathematics, used for modeling...

Optimization problems over rearrangement classes arise in various areas such as mathematics, fluid mechanics, biology, and finance. When the generator of the rearrangement class is two-valued, they reduce to shape optimization and free boundary problems which can exhibit intriguing symmetry breaking phenomena. A robust framework is required for com...

Optimization problems over rearrangement classes arise in various areas such as mathematics, fluid mechanics, biology, and finance. When the generator of the rearrangement class is two-valued, they reduce to shape optimization and free boundary problems which can exhibit intriguing symmetry breaking phenomena. A robust framework is required for com...

We discuss a parametric eigenvalue problem, where the differential operator is of \((p,2)\)-Laplacian type. We show that, when \(p\neq 2\), the spectrum of the operator is a half line, with the end point formulated in terms of the parameter and the principal eigenvalue of the Laplacian with zero Dirichlet boundary conditions. Two cases are consider...

Hybrid systems---more precisely, their mathematical models---can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability---namely, the reflexive and transitive closure of a transition relation---can be unsafe, i.e., it may...

We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For t...

We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for general smooth bounded domains, and derive a symmetry result for radial ones. We strengthen our analysis by prov...

In this note, we consider a control theory problem involving a strictly convex energy functional, which is not Gâteaux differentiable. The functional came up in the study of a shape optimization problem, and here we focus on the minimization of this functional. We relax the problem in two different ways and show that the relaxed variants can be sol...

The material in this paper has been divided into two main parts. In the first part we describe two optimization problems—one maximization and one minimization—related to a sharp trace inequality that was recently obtained by G. Auchmuty. In both problems the admissible set is the one comprising characteristic functions whose supports have a fixed m...

We study the existence and uniqueness of positive solutions to
a class of nonlocal boundary-value problems involving the p-Laplacian.
Our main tools are a variant of the Schaefer's fixed point theorem,
an inequality which suitably handles the p-Laplacian operator, and
a Sobolev embedding which is applicable to the bounded domain.

In this paper we introduce two rearrangement optimization problems, one being a maximization and the other a minimization problem, related to a nonlocal boundary value problem of Kirchhoff type. Using the theory of rearrangements as developed by G. R. Burton we are able to show that both problems are solvable, and derive the corresponding optimalit...

In this paper we introduce a boundary value problem involving powers of the p-Laplace operator. We will then prove a variant of Talenti inequality which shows that the Schwarz symmetrization of the solution of the boundary value problem is majorized by the solution of the appropriately symmetrized version of the problem. The case of equality is als...

In this note we study a function which frequently appears in partial differential equations. We prove that this function is absolutely continuous, hence it can be written as a definite integral. As a result we obtain some estimates regarding solutions of the Hamilton-Jacobi systems.

In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the di...

We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (...

In this paper we will discuss three different problems which share the same conclusions. In the first one we revisit the well known Faber-Krahn inequality for the principal eigenvalue of the p-Laplace operator with zero homogeneous Dirichlet boundary conditions. Motivated by Chatelain, Choulli, and Henrot, 1996, we show in case the equality holds i...

Kolmogorov complexity was originally defined for finitely-representable objects. Later, the definition was extended to real numbers based on the asymptotic behaviour of the sequence of the Kolmogorov complexities of the finitely-representable objects—such as rational numbers—used to approximate them.
This idea will be taken further here by extendi...

Domain theory has been used with great success in providing a semantic framework for Turing computability, over both discrete and continuous spaces. On the other hand, classical approximation theory provides a rich set of tools for computations over real functions with (mainly) polynomial and rational function approximations.
We present a semantic...

Kolmogorov complexity was originally defined for finitely-representable objects. Later, the definition was extended to real
numbers based on the behaviour of the sequence of Kolmogorov complexities of finitely-representable objects—such as rational
numbers—used to approximate them. The idea will be taken further here by extending the definition to...

One of the basic features of life is replication. Indeed one of the three components of evolution is inheritance, which implies some similarity (both phenotypic and genotypic) between parents and offspring. Life is a process and not a substance (e.g. being carbon-based does not capture what life is), and this therefore justifies an algorithmic defi...

We develop and study the concept of dataflow process networks as used for example by Kahn to suit exact computation over data types related to real numbers, such as continuous functions and geometrical solids. Furthermore, we consider communicating these exact objects among processes using protocols of a query-answer nature as introduced in our ear...

We address the question of how to communicate among distributed processes values such as real numbers, continuous functions and geometrical solids with arbitrary precision, yet efficiently. We extend the established concept of lazy communication using streams of approximants by introducing explicit queries. We formalise this approach using protocol...

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by
Edalat and Pattinson [1]. Compared to Edalat and Pattinson’s implementation, our algorithm uses a more efficient arithmetic
based on an arbitrary precision floating-point library. Despite the additional overestimations due to f...

Since Di Gianantonio [1993] introduced his semantics for exact real number computation, there has always been a struggle to
maintain data abstraction and efficiency as much as possible. The interval domain model-or its variations-can be regarded
as the standard setting to obtain maximum data abstraction. As for efficiency there has been much focus...

Since Di Gianantonio introduced his semantics for exact real number computation, there has always been a struggle to maintain
data abstraction and efficiency as much as possible. The interval domain model —or its variations— can be regarded as the
standard setting to obtain maximum data abstraction. As for efficiency there has been much focus on se...

Abstract Real PCF(RPCF) was proposed by Mart·n Escard· o [Esc97] as a language for Real number computation. One of the key ó and most controversial ó constants is parallel-if (pif I), the existence of which causes a serious ine ciency in the language leading to RPCF being impractical. While search is being undertaken to replace pifI with a more e c...

Real PCF(RPCF) was proposed by Martín Escardó [Esc97] as a language for Real number computation. One of the key — and most controversial — constants is parallel-if (pif I), the existence of which causes a serious inefficiency in the language leading to RPCF being impractical. While search is being undertaken to replace pif I with a more efficient o...

We adjust the concept of dataflow process networks as used for example by Kahn to suit exact computation over data types related to real numbers, such as continuous functions and geometrical solids. Furthermore, we consider communicating these exact objects among pro-cesses using protocols of a query-answer nature. This enables processes to provide...

We adapt the concept of dataflow process network to suit computation with real numbers and other data types that require approximation, providing a framework for com- positional distributed exact computation with these data types. Our processes communicate approximations with each other in a lazy request-response manner, which is ad- vantageous for...

SPARK is an environment for the development and validation of soft-ware for high integrity applications. So far the SPARK annotation language and tool set have lacked explicit support for floating point arithmetic. This paper de-scribes ongoing work extending the annotation language to support analysis and proof of functional properties and excepti...

A domain-theoretical denotational framework is provided in which the behaviour of networks can be analysed and studied compositionally. The networks considered here are discrete-time with a global clock and the communication on each channel adheres to some query-response protocol, leading to a form of lazy evaluation. Although the setting is pre-se...

It is already known from the previous works done by Escar o, Streicher and Hofmann ([EHS98]) and my own previous result ([Far]) that without any parallel mechanism, even basic first-order functions on real numbers -such as addition, exponential function, or in fact any non-sequential or non-affine function -are not definable in Real-PCF. However, i...