Imperial College London

ProfessorAbbasEdalat

Faculty of EngineeringDepartment of Computing

Professor in Computer Science & Maths
 
 
 
//

Contact

 

+44 (0)20 7594 8245a.edalat Website

 
 
//

Location

 

420Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Publication Type
Year
to

122 results found

Edalat A, Farjudian A, Li Y, 2023, Recursive solution of initial value problems with temporal discretization, Theoretical Computer Science, Vol: 980, ISSN: 0304-3975

We construct a continuous domain, as a model of interval analysis, for temporal discretization of differential equations. By using this domain, and the domain of Lipschitz maps, we formulate a generalization of the Euler operator, which exhibits second-order convergence. We prove computability of the operator within the framework of effectively given domains. The operator only requires the vector field of the differential equation to be Lipschitz continuous, in contrast to the related operators in the literature which require the vector field to be at least continuously differentiable. Within the same framework, we also analyze temporal discretization and computability of another variant of the Euler operator formulated according to Runge-Kutta theory. We prove that, compared with this variant, the second-order operator that we formulate directly, not only imposes weaker assumptions on the vector field, but also exhibits superior convergence rate. We implement the first-order, second-order, and Runge-Kutta Euler operators using arbitrary-precision interval arithmetic, and report on some experiments. The experiments confirm our theoretical results. In particular, we observe the superior convergence rate of our second-order operator compared with the Runge-Kutta Euler and the common (first-order) Euler operators.

Journal article

Law AJ, Hu R, Alazraki L, Edalat A, Gopalan A, Polydorou Net al., 2023, A multilingual virtual guide for self-attachment technique, Online, 2022 IEEE Fourth International Conference on Cognitive Machine Intelligence CogMI 2022, Publisher: IEEE, Pages: 107-116

In this work, we propose a computational framework that leverages existing out-of-language data to create a conversational agent for the delivery of self-attachment technique in Mandarin. Our framework does not require large-scale human translations, yet it achieves a comparable performance whilst also maintaining safety and reliability. We propose two different methods of augmenting available response data through empathetic rewriting. We evaluate our chatbot against a previous, English-only SAT chatbot through non-clinical human trials (N=42), each lasting five days, and quantitatively show that we are able to attain a comparable level of performance to the English SAT chatbot. We provide qualitative analysis on the limitations of our study and suggestions with the aim of guiding future improvements.

Conference paper

Millea A, Edalat A, 2023, Using deep reinforcement learning with hierarchical risk parity for portfolio optimization, International Journal of Financial Studies, Vol: 11, ISSN: 2227-7072

We devise a hierarchical decision-making architecture for portfolio optimization on multiple markets. At the highest level a Deep Reinforcement Learning (DRL) agent selects among a number of discrete actions, representing low-level agents. For the low-level agents, we use a set of Hierarchical Risk Parity (HRP) and Hierarchical Equal Risk Contribution (HERC) models with different hyperparameters, which all run in parallel, off-market (in a simulation). The information on which the DRL agent decides which of the low-level agents should act next is constituted by the stacking of the recent performances of all agents. Thus, the modelling resembles a statefull, non-stationary, multi-arm bandit, where the performance of the individual arms changes with time and is assumed to be dependent on the recent history. We perform experiments on the cryptocurrency market (117 assets), on the stock market (46 assets) and on the foreign exchange market (28 pairs) showing the excellent robustness and performance of the overall system. Moreover, we eliminate the need for retraining and are able to deal with large testing sets successfully.

Journal article

Edalat A, Farsinezhad M, Bokharaei M, Judy Fet al., 2022, A pilot study to evaluate the efficacy of self-attachment to treat chronic anxiety and/or depression in Iranian women, International Journal of Environmental Research and Public Health, Vol: 19, ISSN: 1660-4601

The aim of this pilot study was to evaluate the efficacy of the new Self-Attachment Technique (SAT) in treating resistant anxiety and depression, lasting at least three years, among Iranian women from different social backgrounds. In this intervention, the participant, using their childhood photos, imaginatively creates an affectional bond with their childhood self, vows to consistently support and lovingly re-raise this child to emotional well-being. We conducted a longitudinal study with repeated measurement to evaluate the efficacy of SAT using ANOVA. Thirty-eight women (N=30) satisfying the inclusion and exclusion criteria were recruited from different parts of Tehran. To describe the SAT protocols, a total of eight one-to-one sessions were offered to the recruits, the first four were weekly while the last four were fortnightly. The participants were expected to practice the protocols for twenty minutes twice a day. Two questionnaires, GAD-7 and PHQ-9, were used to measure anxiety and depression levels before and after the intervention and in a three-month follow-up. Thirty women completed the course. The change in the anxiety level between the pre-test and the post-test was significant at p<0.001 with effect size 2.6. The change in anxiety between pre-test and follow-up test was also significant at p<0.001 with effect size 3.0 respectively. The change in anxiety between the post-test and the follow-up was significant at p<0.05 with effect size 0.6. For depression, the change between the pre-test and the post-test or the follow-up was significant at p<0.001 with effect size 2.5 for each.

Journal article

Alazraki L, Ghachem A, Polydorou N, Khosmood F, Edalat Aet al., 2022, An empathetic AI coach for self-attachment therapy, 2021 IEEE Third International Conference on Cognitive Machine Intelligence (CogMI), Publisher: IEEE, Pages: 78-87

In this work, we present a new dataset and acomputational strategy for a digital coach that aims to guideusers in practicing the protocols of self-attachment therapy.Our framework augments a rule-based conversational agentwith a deep-learning classifier for identifying the underlyingemotion in a user’s text response, as well as a deep-learningassisted retrieval method for producing novel, fluent andempathetic utterances. We also craft a set of human-likepersonas that users can choose to interact with. Our goal isto achieve a high level of engagement during virtual therapysessions. We evaluate the effectiveness of our framework ina non-clinical trial with N=16 participants, all of whom havehad at least four interactions with the agent over the courseof five days. We find that our platform is consistently ratedhigher for empathy, user engagement and usefulness than thesimple rule-based framework. Finally, we provide guidelines tofurther improve the design and performance of the application,in accordance with the feedback received.

Conference paper

Gotsman T, Polydorou N, Edalat A, 2022, Valence/arousal estimation of occluded faces from VR headsets, 2021 IEEE Third International Conference on Cognitive Machine Intelligence (CogMI), Publisher: IEEE, Pages: 96-105

Emotion recognition from facial visual signals is a challenge which has attracted enormous interest over the past two decades. Researchers are attempting to teach computers to better understand a person’s emotional state. Providing emotion recognition can massively enrich experiences. The benefits of this research for human–computer interactions are limitless. Emotions are intricate, and so we need a representative model of the full spectrum displayed by humans. A multi-dimensional emotion representation, which includes valence (how positive an emotion) and arousal (how calming or exciting an emotion), is a good fit. Virtual Reality (VR), a fully immersive computer-generated world, has witnessed significant growth over the past years. It has a wide range of applications including in mental health, such as exposure therapy and the self-attachment technique. In this paper, we address the problem of emotion recognition when the user is immersed in VR. Understanding emotions from facial cues is in itself a demanding task. It is made even harder when a head-mounted VR headset is worn, as now an occlusion blocks the upper half of the face. We attempt to overcome this issue by introducing EmoFAN-VR, a deep neural network architecture, to analyse facial affect in the presence of a severe occlusion from a VR headset with a high level of accuracy. We simulate an occlusion representing a VR headset and apply it to all datasets in this work. EmoFAN-VR predicts both discrete and continuous emotions in one step, meaning it can be used in real-time deployment. We fine-tune our network on the AffectNet dataset under VR occlusion and test it on the AFEW-VA dataset, setting a new baseline for this dataset whilst under VR occlusion.

Conference paper

Edalat A, 2022, Smooth approximation of Lipschitz maps and their subgradients, Journal of the ACM, Vol: 69, Pages: 1-32, ISSN: 0004-5411

We derive new representations for the generalised Jacobian of a locally Lipschitz map between finite dimensional real Euclidean spaces as the lower limit (i.e., limit inferior) of the classical derivative of the map where it exists. The new representations lead to significantly shorter proofs for the basic properties of the subgradient and the generalised Jacobian including the chain rule. We establish that a sequence of locally Lipschitz maps between finite dimensional Euclidean spaces converges to a given locally Lipschitz map in the L-topology—that is, the weakest refinement of the sup norm topology on the space of locally Lipschitz maps that makes the generalised Jacobian a continuous functional—if and only if the limit superior of the sequence of directional derivatives of the maps in a given vector direction coincides with the generalised directional derivative of the given map in that direction, with the convergence to the limit superior being uniform for all unit vectors. We then prove our main result that the subspace of Lipschitz C∞ maps between finite dimensional Euclidean spaces is dense in the space of Lipschitz maps equipped with the L-topology, and, for a given Lipschitz map, we explicitly construct a sequence of Lipschitz C∞ maps converging to it in the L-topology, allowing global smooth approximation of a Lipschitz map and its differential properties. As an application, we obtain a short proof of the extension of Green’s theorem to interval-valued vector fields. For infinite dimensions, we show that the subgradient of a Lipschitz map on a Banach space is upper continuous, and, for a given real-valued Lipschitz map on a separable Banach space, we construct a sequence of Gateaux differentiable functions that converges to the map in the sup norm topology such that the limit superior of the directional derivatives in any direction coincides with the generalised directional derivative of the Lipschitz map in that direction.

Journal article

Polydorou N, Edalat A, 2021, An interactive VR platform with emotion recognition for self-attachment intervention, EAI Endorsed Transactions on Pervasive Health and Technology, Vol: 7, Pages: 1-14

INTRODUCTION: Self-attachment is a new self-administrable psychotherapeutic intervention based on creating an affectional bond between the user and their childhood-self using their childhood photos to develop the capacity for affect self-regulation. Technological advances, such as virtual reality (VR), can enhance the procedure of this intervention and make it scalable.METHODS: We have developed a user-friendly, interactive VR platform for self-attachment featuring a virtual assistant and a customised child avatar that resembles the user in their childhood. The virtual agent interacts with the user and using an emotion recognition algorithm can provide suggestions for the user to undertake an appropriate self-attachment sub-protocol. Furthermore, the platform allows user interaction with the child avatar, such as embracing the avatar.RESULTS: We show by a small preliminary trial that such a VR experience can be realistic, leading to a positive emotion change in the user.

Journal article

Edalat A, Farjudian A, Mohammadian M, Patinson Det al., 2020, Domain theoretic second-order Euler’s method for solving initial valueproblems, Mathematical Foundations of Programming Semantics, Publisher: Elsevier, Pages: 105-128, ISSN: 1571-0661

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 may be complete, i.e., the result may be obtained to any degree of accuracy. Furthermore, unlike methods based on interval arithmetic which require access to the syntactic representation of the vector field, domain-theoretic methods only deal with the semantics of the field, in the sense that the field is assumed to be given via finitely-representable approximations, to within any required accuracy.In contrast to the domain-theoretic first-order Euler method, the second-order method uses the local Lipschitz properties of the field. This is achieved by using a domain for Lipschitz functions, whose elements are consistent pairs that provide approximations of the field and its local Lipschitz properties. In the special case where the field is differentiable, the local Lipschitz properties are exactly the local differential properties of the field. In solving IVPs, Lipschitz continuity of the field is a common assumption, as a sufficient condition for uniqueness of the solution. While the validated methods for solving IVPs commonly impose further restrictions on the vector field, the second-order Euler method requires no further condition. In this sense, the method may be seen as the most general of its kind.To avoid complicated notations and lengthy arguments, the results of the paper are stated for the second-order Euler method. Nonetheless, the framework, and the results, may be extended to any higher-order Euler method, in a straightforward way.

Conference paper

Davari MJ, Edalat A, Lieutier A, 2020, The convex hull of finitely generable subsets and its predicate transformer, Thirty-Fourth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Publisher: ACM/IEEE

We consider the domain of non-empty convex andcompact subsets of a finite dimensional Euclidean space torepresent partial or imprecise points in Computational Geom-etry. The convex hull map on such imprecise points is givendomain-theoretically by an inner and an outer convex hull. Weprovide a practical algorithm to compute the inner convex hullwhen there are a finite number of convex polytopes as partialpoints. A notion of pre-inner support function is introduced,whose convex hull gives the support function of the innerconvex hull in a general setting. We then show that the convexhull map is Scott continuous and can be extended to finitelygenerable subsets, represented by the Plotkin power domain ofthe underlying domain. This in particular allows us to computethe convex hull of attractors of iterated function systems infractal geometry. Finally, we derive a program logic for theconvex hull map in the sense of the weakest pre-condition fora given post-condition.

Conference paper

Ghaznavi I, Gillies D, Nicholls D, Edalat Aet al., 2020, Photorealistic avatars to enhance the efficacy of Self-attachment psychotherapy, 3rd IEEE International Conference on Artificial Intelligence and Virtual Reality (IEEE AIVR), Publisher: IEEE COMPUTER SOC, Pages: 60-67

Conference paper

Edalat A, Ghorban S, Ghoroghi A, 2018, Ex Post Nash Equilibrium in Linear Bayesian Games for Decision Making in Multi-Environments, Games, Vol: 9, ISSN: 2073-4336

We show that a Bayesian game where the type space of each agent is a bounded set of m-dimensional vectors with non-negative components and the utility of each agent depends linearly on its own type only is equivalent to a simultaneous competition in m basic games which is called a uniform multigame. The type space of each agent can be normalised to be given by the ( m - 1 ) -dimensional simplex. This class of m-dimensional Bayesian games, via their equivalence with uniform multigames, can model decision making in multi-environments in a variety of circumstances, including decision making in multi-markets and decision making when there are both material and social utilities for agents as in the Prisoner’s Dilemma and the Trust Game. We show that, if a uniform multigame in which the action set of each agent consists of one Nash equilibrium inducing action per basic game has a pure ex post Nash equilibrium on the boundary of its type profile space, then it has a pure ex post Nash equilibrium on the whole type profile space. We then develop an algorithm, linear in the number of types of the agents in such a multigame, which tests if a pure ex post Nash equilibrium on the vertices of the type profile space can be extended to a pure ex post Nash equilibrium on the boundary of its type profile space in which case we obtain a pure ex post Nash equilibrium for the multigame.

Journal article

Edalat A, Maleki M, 2018, Differential calculus with imprecise input and its logical framework, International Conference on Foundations of Software Science and Computation Structures 2018, Publisher: Springer International Publishing, Pages: 459-475

We develop a domain-theoretic Differential Calculus for locally Lipschitz functions on finite dimensional real spaces with imprecise input/output. The inputs to these functions are hyper-rectangles and the outputs are compact real intervals. This extends the domain of application of Interval Analysis and exact arithmetic to the derivative. A new notion of a tie for these functions is introduced, which in one dimension represents a modification of the notion previously used in the one-dimensional framework. A Scott continuous sub-differential for these functions is then constructed, which satisfies a weaker form of calculus compared to that of the Clarke sub-gradient. We then adopt a Program Logic viewpoint using the equivalence of the category of stably locally compact spaces with that of semi-strong proximity lattices. We show that given a localic approximable mapping representing a locally Lipschitz map with imprecise input/output, a localic approximable mapping for its sub-differential can be constructed, which provides a logical formulation of the sub-differential operator.

Conference paper

Cittern D, Nolte T, Friston K, Edalat Aet al., 2018, Intrinsic and extrinsic motivators of attachment under active inference, PLoS ONE, Vol: 13, ISSN: 1932-6203

rs Metrics Comments Media Coverage Abstract Introduction Materials and methods Results Discussion Supporting information Acknowledgments References Reader Comments (0) Media Coverage (0) FiguresAbstractThis paper addresses the formation of infant attachment types within the context of active inference: a holistic account of action, perception and learning in the brain. We show how the organised forms of attachment (secure, avoidant and ambivalent) might arise in (Bayesian) infants. Specifically, we show that these distinct forms of attachment emerge from a minimisation of free energy—over interoceptive states relating to internal stress levels—when seeking proximity to caregivers who have a varying impact on these interoceptive states. In line with empirical findings in disrupted patterns of affective communication, we then demonstrate how exteroceptive cues (in the form of caregiver-mediated AMBIANCE affective communication errors, ACE) can result in disorganised forms of attachment in infants of caregivers who consistently increase stress when the infant seeks proximity, but can have an organising (towards ambivalence) effect in infants of inconsistent caregivers. In particular, we differentiate disorganised attachment from avoidance in terms of the high epistemic value of proximity seeking behaviours (resulting from the caregiver’s misleading exteroceptive cues) that preclude the emergence of coherent and organised behavioural policies. Our work, the first to formulate infant attachment in terms of active inference, makes a new testable prediction with regards to the types of affective communication errors that engender ambivalent attachment.

Journal article

Cittern D, Edalat A, 2017, A neural model of empathic states in attachment-based psychotherapy, Computational Psychiatry, Vol: 1, Pages: 132-167, ISSN: 2379-6227

We build on a neuroanatomical model of how empathic states can motivatecaregiving behaviour, via empathy circuit-driven activation of regions in thehypothalamus and amygdala which in turn stimulate a mesolimbic-ventral pal-lidum pathway, by integrating findings related to the perception of pain in selfand others. Based on this we propose a network to capture states of personaldistress and empathic concern, which are particularly relevant for psychothera-pists conducting attachment-based interventions. This model is then extendedfor the case of Self-Attachment therapy in which conceptualised components ofthe self serve as both the source of and target for empathic resonance, and weconsider how states of empathic concern involving an other that is perceived asbeing closely related to the self might enhance the motivation for self-directedbonding. We simulate our model computationally, and discuss the interplaybetween the bonding and empathy protocols of the therapy.

Journal article

Edalat A, Maleki M, 2017, Differentiation in logical form, Logic in Computer Science (LICS 2017), Publisher: ACM / IEEE

We introduce a logical theory of differentiation for areal-valued function on a finite dimensional real Euclidean space.A real-valued continuous function is represented by a localic ap-proximable mapping between two semi-strong proximity lattices,representing the two stably locally compact Euclidean spaces forthe domain and the range of the function. Similarly, the Clarkesubgradient, equivalently the L-derivative, of a locally Lipschitzmap, which is non-empty, compact and convex valued, is repre-sented by an approximable mapping. Approximable mappings ofthe latter type form a bounded complete domain isomorphic withthe function space of Scott continuous functions of a real variableinto the domain of non-empty compact and convex subsets ofthe finite dimensional Euclidean space partially ordered withreverse inclusion. Corresponding to the notion of a single-tie ofa locally Lipschitz function, used to derive the domain-theoreticL-derivative of the function, we introduce the dual notion ofa single-knot of approximable mappings which gives rise toLipschitzian approximable mappings. We then develop the notionof a strong single-tie and that of a strong knot leading to aStone duality result for locally Lipschitz maps and Lipschitzianapproximable mappings. The strong single-knots, in which aLipschitzian approximable mapping belongs, are employed todefine the Lipschitzian derivative of the approximable mapping.The latter is dual to the Clarke subgradient of the correspondinglocally Lipschitz map defined domain-theoretically using strongsingle-ties. A stricter notion of strong single-knots is subsequentlydeveloped which captures approximable mappings of continu-ously differentiable maps providing a gradient Stone dualityfor these maps. Finally, we derive a calculus for Lipschitzianderivative of approximable mapping for some basic constructorsand show that it is dual to

Conference paper

Bilokon P, Edalat A, 2017, A domain-theoretic approach to Brownian motion and general continuous stochastic processes, Theoretical Computer Science, Vol: 691, Pages: 10-26, ISSN: 0304-3975

We introduce a domain-theoretic framework for continuous-time, continuous-statestochastic processes. The laws of stochastic processes are embedded into the spaceof maximal elements of the normalised probabilistic power domain on the space ofcontinuous interval-valued functions endowed with the relative Scott topology. We usethe resultingω-continuous bounded complete dcpo to obtain partially defined stochas-tic processes and characterise their computability. For a given continuous stochasticprocess, we show how its domain-theoretic, i.e., finitary, approximations can be con-structed, whose least upper bound is the law of the stochastic process. As a mainresult, we apply our methodology to Brownian motion. We construct a partially de-fined Wiener measure and show that the Wiener measure is computable within thedomain-theoretic framework.

Journal article

Cittern D, Edalat A, Ghaznavi I, 2017, An immersive virtual reality mobile platform for self-attachment, Artificial Intelligence and Simulation of Behaviour (AISB) 2017, Publisher: AISB

Psychotherapy is among the most effective techniques forcombating mental health issues, and virtual reality is beginning to beexplored as a way to enhance the efficacy of various psychotherapeu-tic treatments. In this paper we propose an immersive virtual realitymobile platform for Self-Attachment psychotherapy. Under the Self-Attachment therapeutic framework, the causes of disorders such aschronic anxiety and depression are traced back to the quality of theindividual’s attachment with their primary caregiver during child-hood. Our proposed platform aims to assist the user in enhancingtheir capacities for self-regulation of emotion, by means of earningsecure attachment through the experience of positive attachment in-teractions, missed in their childhood. In the virtual environment pro-vided by the platform, the adult-self of the user learns to create andstrengthen an affectional and supportive bond with the inner-child.It is hypothesised that by long term potentiation and neuroplasticity,the user gradually develops new neural pathways and matures intoan effective secure attachment object for the inner-child, thereby en-abling the self-regulation of emotions.

Conference paper

Edalat A, 2017, Self attachment: A holistic approach to computational psychiatry, Computational Neurology and Psychiatry, Editors: Peter, Bhattacharya, Cochran, Publisher: Springer, Pages: 273-314, ISBN: 9783319499581

There has been increasing evidence to suggest that the root cause of muchmental illness lies in a sub-optimal capacity for affect regulation. Cognition andemotion are intricately linked and cognitive deficits, which are characteristic ofmany psychiatric conditions, are often driven by affect dysregulation, which itselfcan usually be traced back to sub-optimal childhood development. This view is supported by Attachment Theory, a scientific paradigm in developmental psychology,that classifies the type of relationship a child has with a primary care-giver to one offour types of insecure or secure attachments. Individuals with insecure attachment intheir childhoods are prone to a variety of mental illness, whereas a secure attachmentin childhood provides a secure base in life. We therefore propose, based on previouswork, a holistic approach to Computational Psychiatry, which is informed by thedevelopment of the brain during infancy in social interaction with its primary care-givers. We identify the protocols governing the interaction of a securely attachedchild with its primary care-givers that produce the capacity for affect regulation inthe child. We contend that these protocols can be self-administered to construct,by neuroplasticity and long term potentiation, new “optimal” neural pathways inthe brains of adults with insecure attachment history. This procedure is called Self-attachment and aims to help individuals create their own attachment objects whichhas many parallels with Winnicott’s notion of transitional object, Bowlby’s comfort objects, Kohut’s empathetic self-object as well as religion as an attachment object. We describe some mathematical models for Self-attachment: a game-theoreticmodel, a model based on the notion of a strong pattern in an energy based associativeneural network and several neural models of the human brain.

Book chapter

Edalat A, 2017, Decidability of consistency of function and derivative information for a triangle and a convex quadrilateral, Departmental Technical Report: 17/7, Publisher: Department of Computing, Imperial College London, 17/7

Given a triangle in the plane, a planar convex compact set and an upper and and a lower bound, wederive a linear programming algorithm which checks if there exists a real-valued Lipschitz map definedon the triangle and bounded by the lower and upper bounds, whose Clarke subgradient lies within theconvex compact set. We show that the problem is in fact equivalent to finding a piecewise linear surfacewith the above property. We extend the result to a convex quadrilateral in the plane. In addition, weobtain some partial results for this problem in higher dimensions.

Report

Edalat A, 2017, Self-attachment: A self-administrable intervention for chronic anxiety and depression, Departmental Technical Report: 17/3, Publisher: Department of Computing, Imperial College London, 17/3

There has been increasing evidence to suggest that the root cause of muchmental illness lies in a sub-optimal capacity for affect regulation. Cognition andemotion are intricately linked and cognitive deficits, which are characteristic ofmany psychiatric conditions, are often driven by affect dysregulation, which itselfcan usually be traced back to sub-optimal childhood development as supported byAttachment Theory. Individuals with insecure attachment types in their childhoodsare prone to a variety of mental illness, whereas a secure attachment type in childhoodprovides a secure base in life. We therefore propose a holistic approach totackle chronic anxiety and depression, typical of Axis II clinical disorders, whichis informed by the development of the infant brain in social interaction with itsprimary care-givers. We formulate, in a self-administrable way, the protocols governingthe interaction of a securely attached child with its primary care-givers thatproduce the capacity for affect regulation in the child. We posit that these protocolsconstruct, by neuroplasticity and long term potentiation, new optimal neuralpathways in the brains of adults with insecure childhood attachment that sufferfrom mental disorder. This procedure is called self-attachment and aims to helpthe individuals to create their own attachment objects in the form of their adult selflooking after their inner child.

Report

Edalat A, Maleki M, 2017, Differentiation in logical form, Departmental Technical Report: 17/6, Publisher: Department of Computing, Imperial College London, 17/6

We introduce a logical theory of differentiation for areal-valued function on a finite dimensional real Euclidean space.A real-valued continuous function is represented by a localic approximablemapping between two semi-strong proximity lattices,representing the two stably locally compact Euclidean spaces forthe domain and the range of the function. Similarly, the Clarkesubgradient, equivalently the L-derivative, of a locally Lipschitzmap, which is non-empty, compact and convex valued, is representedby an approximable mapping. Approximable mappings ofthe latter type form a bounded complete domain isomorphic withthe function space of Scott continuous functions of a real variableinto the domain of non-empty compact and convex subsets ofthe finite dimensional Euclidean space partially ordered withreverse inclusion. Corresponding to the notion of a single-tie ofa locally Lipschitz function, used to derive the domain-theoreticL-derivative of the function, we introduce the dual notion ofa single-knot of approximable mappings which gives rise toLipschitzian approximable mappings. We then develop the notionof a strong single-tie and that of a strong knot leading to aStone duality result for locally Lipschitz maps and Lipschitzianapproximable mappings. The strong single-knots, in which aLipschitzian approximable mapping belongs, are employed todefine the Lipschitzian derivative of the approximable mapping.The latter is dual to the Clarke subgradient of the correspondinglocally Lipschitz map defined domain-theoretically using strongsingle-ties. A stricter notion of strong single-knots is subsequentlydeveloped which captures approximable mappings of continuouslydifferentiable maps providing a gradient Stone dualityfor these maps. Finally, we derive a calculus for Lipschitzianderivative of approximable mapping for some basic constructorsand show that it is dual to the calculus satisfied by the Clarkesubgradient.

Report

White J, Edalat A, 2016, Iran is ready to thrive, NEW SCIENTIST, Vol: 229, Pages: 29-29, ISSN: 0262-4079

Journal article

Edalat A, 2015, Introduction to self-attachment and its neural basis, The 2015 International Joint Conference on Neural Networks (IJCNN), Publisher: IEEE, Pages: 1-8

We introduce the notion of self-attachment which, based on an interdisciplinary set of concepts, proposes a new psychotherapeutic technique. The underlying ideas include findings and paradigms in developmental psychology and neuroscience, neuroplasticity and long term term potentiation, fMRI studies on human bond making, ethology and psychology of religion and experiments in energy based artificial neural networks. The proposed self-attachment therapeutic technique is distinguished by its intervention to create an internal and passionate affectional bond within the individual between the “adult self”, representing the logical and cognitive faculty, and the “inner child”, representing the unregulated and undeveloped emotional circuits. The aim is to create more optimal circuits for emotional regulation. The proposed self-attachment protocols internally emulate within the individual the interactions of a good enough primary care-giver and child in order to moderate the child’s arousal level, minimise its negative affects and maximize its positive affects. These interactions are assumed, in developmental neuroscience and in developmental psychology, to be the basis of secure attachment of children with their parents, which leads to an optimal regulation of neurotransmitters, hormones, and the emotional dynamics of the individual. We report on several case studies of this technique in recent years. Finally, we propose a simple mathematical model to capture the impact of self-attachment protocols using the notion of strong patterns in energy based neural networks and employ a recently developed mathematical model to examine the impact of self-attachment using emotional and ognitive neural pathways for decision making.

Conference paper

Cittern D, Edalat A, 2015, Towards a Neural Model of Bonding in Self-Attachment, International Joint Conference on Neural Networks (IJCNN), Publisher: IEEE, ISSN: 2161-4393

Conference paper

Cittern D, Edalat A, 2015, Reinforcement Learning for Nash Equilibrium Generation, Autonomous Agents and Multiagent Systems (AAMAS), Publisher: International Foundation for Autonomous Agents and Multiagent Systems, Pages: 1727-1728

Conference paper

Edalat A, 2015, Extensions of domain maps in differential and integral calculus, Logic in Computer Science (LICS) 2015, Publisher: IEEE, Pages: 426-437, ISSN: 1043-6871

We introduce in the context of differential and integral calculus several key extensions of higher order maps from a dense subset of a topological space into a continuous Scott domain. These higher order maps include the classical derivative operator and the Riemann integration operator. Using a sequence of test functions, we prove that the subspace of real-valued continuously differentiable functions on a finite dimensional Euclidean space is dense in the space of Lipschitz maps equipped with the Ltopology. This provides a new result in basic mathematical analysis, which characterises the L-topology in terms of the limsup of the sequence of derivatives of a sequence of C1 maps that converges to a Lipschitz map. Using this result, it is also shown that the generalised (Clarke) gradient on Lipschitz maps is the extension of the derivative operator on C1 maps. We show that the generalised Riemann integral (R-integral) of a real-valued continuous function on a compact metric space with respect to a Borel measure can be extended to the integral of interval-valued functions on the metric space with respect to valuations on the probabilistic power domain of the space of non-empty and compact sets of the metric space. We also prove that the Lebesgue integral operator on integrable functions is the extension of the R-integral operator on continuous functions. We finally illustrate an application of these results by deriving a simple proof of Green’s theorem for interval-valued vector fields.

Conference paper

Edalat A, 2014, A derivative for complex Lipschitz maps with generalised Cauchy–Riemann equations, Theoretical Computer Science, Vol: 564, Pages: 89-106, ISSN: 0304-3975

We introduce the Lipschitz derivative or the L-derivative of a locally Lipschitz complex map: it is a Scott continuous, compact and convex set-valued map that extends the classical derivative to the bigger class of locally Lipschitz maps and allows an extension of the fundamental theorem of calculus and a new generalisation of Cauchy–Riemann equations to these maps, which form a continuous Scott domain. We show that a complex Lipschitz map is analytic in an open set if and only if its L-derivative is a singleton at all points in the open set. The calculus of the L-derivative for sum, product and composition of maps is derived. The notion of contour integration is extended to Scott continuous, non-empty compact, convex valued functions on the complex plane, and by using the L-derivative, the fundamental theorem of contour integration is extended to these functions.

Journal article

Bilokon P, Edalat A, 2014, A domain-theoretic approach to Brownian motion and general continuous stochastic processes, Twenty-Ninth Annual ACM/IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS), Publisher: ACM

We introduce a domain-theoretic framework for continuous-time,continuous-state stochastic processes. The laws of stochastic processesare embedded into the space of maximal elements of thenormalised probabilistic power domain on the space of continuousinterval-valued functions endowed with the relative Scott topology.We use the resulting !-continuous bounded complete dcpo to definepartial stochastic processes and characterise their computability.For a given continuous stochastic process, we show how itsdomain-theoretic, i.e., finitary, approximations can be constructed,whose least upper bound is the law of the stochastic process. As amain result, we apply our methodology to Brownian motion. Weconstruct a partial Wiener measure and show that the Wiener measureis computable within the domain-theoretic framework.

Conference paper

Edalat A, Lin Z, 2014, A Neural Model of Mentalization/Mindfulness based Psychotherapy, The 2014 International Joint Conference on Neural Networks (IJCNN 2014)

We introduce and implement a neural model for mentalization/mindfulness basedpsychotherapy. It uses Dan Levine’s neural model of pathways foremotional-cognitive decision making, which is integratedwith a competitive Hopfield network built up from the new concept of strong patternsfor the six basic emotions and for mentalization ormindfulness. We adopt a particular form of Q-learning toreinforce the mentalizing/mindful pattern in the network,which represents the process of psychotherapy. In a successfulcourse of therapy, the mentalizing/mindful pattern becomes themore dominant pattern compared to negative emotions and thebrain makes decisions that are more deliberate and thoughtfulthan heuristic and automatic.

Conference paper

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.

Request URL: http://wlsprd.imperial.ac.uk:80/respub/WEB-INF/jsp/search-html.jsp Request URI: /respub/WEB-INF/jsp/search-html.jsp Query String: respub-action=search.html&id=00006756&limit=30&person=true