The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

On the inference of agency in operant action: an examination of the cognitive and neural underpinnings in health and schizophrenia

This dissertation elucidates cognitive and neural underpinnings of the sense of agency, which is the feeling that we are in control of our actions and the subsequent consequences. This consciously accessible sensation of control is pervasive, sometimes subtle, and can even be illusory in nature. Furthermore, the experience of self-agency is socially well-shared and considered to be fundamental to human social functioning. It helps people makes sense of the physical and social world around them, to guide and direct them in their goal-directed actions, and to make sense of who does what when they act and react in a social contact. Understanding the roots and occurrence of the experience of agency, then, is an important target in recent psychological and neuroscientific research. The present dissertation aims to contribute to this endeavor by examining how humans produce the conscious experience of agency. The experience of agency over the consequences of actions can be derived from an inference that we make after we see an outcome. Indeed, agency can be inferred when a specific outcome is matched by pre-activated information that is related to the outcome – for instance, if I had the goal to cause a traffic light to turn green by pure force of thought, and it immediately turns green, I will quickly infer and experience myself as the cause of the green light (the subsequent realization that we could not have caused this does not detract from the initial experience). In self-agency inferences, pre-activated information can either be goal-based, when people engage in goal-oriented behavior, and prime-based, where information can be subtly pre-activated in people’s minds by our environment. The present dissertation provides evidence that goal-based and prime-based agency inferences arise from different cognitive mechanisms: whereas goals use attentional control (i.e., working memory) in order to encode, maintain, retrieve and compare information about goals, prime-based agency inferences follow from automatic cognitive accessibility processes that follow the principles of automatic spreading of activation. A second line of research in this dissertation is the first exploration of the neural underpinnings of self-agency inferences. In multiple studies, it has been shown that parietal and frontal brain regions are involved in goal-based self-agency experiences. This observation, together with other research implicates a brain model where a match between a goal and the subsequent outcome is registered in the parietal lobe, and transmitted to the frontal lobe where conscious self-agency experiences are generated. Finally, I investigate the mechanisms underlying self-agency inferences by studying patients with schizophrenia, who as part of their disease often exhibit agency problems, leading to hallucinations and delusions. For these patients, it was found that they report similar goal-based agency experiences as healthy controls, but that they do not use the same brain areas, leading to the notion that agency processing may be less efficient in these patients. Indeed, when patients with schizophrenia only have primes as input for their agency experiences, they appear unable to do so. Future research may elucidate the specific dysfunctioning mechanisms in patients with schizophrenia

On the inference of agency in operant action : an examination of the cognitive and neural underpinnings in health and schizophrenia

This dissertation elucidates cognitive and neural underpinnings of the sense of agency, which is the feeling that we are in control of our actions and the subsequent consequences. This consciously accessible sensation of control is pervasive, sometimes subtle, and can even be illusory in nature. Furthermore, the experience of self-agency is socially well-shared and considered to be fundamental to human social functioning. It helps people makes sense of the physical and social world around them, to guide and direct them in their goal-directed actions, and to make sense of who does what when they act and react in a social contact. Understanding the roots and occurrence of the experience of agency, then, is an important target in recent psychological and neuroscientific research. The present dissertation aims to contribute to this endeavor by examining how humans produce the conscious experience of agency. The experience of agency over the consequences of actions can be derived from an inference that we make after we see an outcome. Indeed, agency can be inferred when a specific outcome is matched by pre-activated information that is related to the outcome – for instance, if I had the goal to cause a traffic light to turn green by pure force of thought, and it immediately turns green, I will quickly infer and experience myself as the cause of the green light (the subsequent realization that we could not have caused this does not detract from the initial experience). In self-agency inferences, pre-activated information can either be goal-based, when people engage in goal-oriented behavior, and prime-based, where information can be subtly pre-activated in people’s minds by our environment. The present dissertation provides evidence that goal-based and prime-based agency inferences arise from different cognitive mechanisms: whereas goals use attentional control (i.e., working memory) in order to encode, maintain, retrieve and compare information about goals, prime-based agency inferences follow from automatic cognitive accessibility processes that follow the principles of automatic spreading of activation. A second line of research in this dissertation is the first exploration of the neural underpinnings of self-agency inferences. In multiple studies, it has been shown that parietal and frontal brain regions are involved in goal-based self-agency experiences. This observation, together with other research implicates a brain model where a match between a goal and the subsequent outcome is registered in the parietal lobe, and transmitted to the frontal lobe where conscious self-agency experiences are generated. Finally, I investigate the mechanisms underlying self-agency inferences by studying patients with schizophrenia, who as part of their disease often exhibit agency problems, leading to hallucinations and delusions. For these patients, it was found that they report similar goal-based agency experiences as healthy controls, but that they do not use the same brain areas, leading to the notion that agency processing may be less efficient in these patients. Indeed, when patients with schizophrenia only have primes as input for their agency experiences, they appear unable to do so. Future research may elucidate the specific dysfunctioning mechanisms in patients with schizophrenia

Attentional Control and Inferences of Agency: Working Memory Load Differentially Modulates Goal-based and Prime-based Agency Experiences

Previous research indicates that people can infer self-agency, the experience of causing outcomes as a result of one’s own actions, in situations where information about action-outcomes is pre-activated through goal-setting or priming. We argue that goal-based agency inferences rely on attentional control that processes information about matches and mismatches between intended and actual outcomes. Prime-based inferences follow an automatic cognitive accessibility process that relies on matches between primed and actual information about outcomes. We tested an improved task for a better examination of goal-based vs. primed-based agency inferences, and examined the moderating effect of working memory load on both types of inferences. Findings of four studies showed that goal-based, but not prime-based agency inferences dwindled under working memory load. These findings suggest that goal-based (vs. primed-based) agency inferences indeed rely on attentional control, thus rendering goal-based agency inferences especially prone to conditions that modulate goal-directed control processes

Abnormal agency experiences in schizophrenia patients : examining the role of psychotic symptoms and familial risk

Experiencing self-agency over one’s own action outcomes is essential for social functioning. Recent research revealed that patients with schizophrenia do not use implicitly available information about their action-outcomes (i.e., prime-based agency inference) to arrive at self-agency experiences. Here, we examined whether this is related to symptoms and/or familial risk to develop the disease. Fifty-four patients, 54 controls, and 19 unaffected (and unrelated) siblings performed an agency inference task, in which experienced agency was measured over action-outcomes that matched or mismatched outcome-primes that were presented before action performance. The Positive and Negative Syndrome Scale (PANSS) and Comprehensive Assessment of Symptoms and History (CASH) were administered to assess psychopathology. Impairments in prime-based inferences did not differ between patients with symptoms of over- and underattribution. However, patients with agency underattribution symptoms reported significantly lower overall self-agency experiences. Siblings displayed stronger prime-based agency inferences than patients, but weaker prime-based inferences than healthy controls. However, these differences were not statistically significant. Findings suggest that impairments in prime-based agency inferences may be a trait characteristic of schizophrenia. Moreover, this study may stimulate further research on the familial basis and the clinical relevance of impairments in implicit agency inferences

Hybrid Computational Intelligence Schemes in Complex Domains: An Extended Review

The increased popularity of hybrid intelligent systems in recent times lies to the extensive success of these systems in many real-world complex problems. The main reason for this success seems to be the synergy derived by the computational intelligent components, such as machine learning, fuzzy logic, neural networks and genetic algorithms. Each of these methodologies provides hybrid systems with complementary reasoning and searching methods that allow the use of domain knowledge and empirical data to solve complex problems. In this paper, we briefly present most of those computational intelligent combinations focusing in the development of intelligent systems for the handling of problems in real-world applications