Strongly Refuting Random CSPs Below the Spectral Threshold

Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be unsatisfiable with high probability. Strong refutation is the problem of certifying that no variable assignment satisfies more than a constant fraction of clauses; this is the natural algorithmic problem in the unsatisfiable regime (when $m/n = \omega(1)$). Intuitively, strong refutation should become easier as the clause density $m/n$ grows, because the contradictions introduced by the random clauses become more locally apparent. For CSPs such as $k$-SAT and $k$-XOR, there is a long-standing gap between the clause density at which efficient strong refutation algorithms are known, $m/n \ge \widetilde O(n^{k/2-1})$, and the clause density at which instances become unsatisfiable with high probability, $m/n = \omega (1)$. In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random $k$-XOR instances with clause density $m/n \ge \widetilde O(n^{(k/2-1)(1-\delta)})$ in time $\exp(\widetilde O(n^{\delta}))$ or in $\widetilde O(n^{\delta})$ rounds of the sum-of-squares hierarchy, for any $\delta \in [0,1)$ and any integer $k \ge 3$. Our algorithms provide a smooth transition between the clause density at which polynomial-time algorithms are known at $\delta = 0$, and brute-force refutation at the satisfiability threshold when $\delta = 1$. We also leverage our $k$-XOR results to obtain strong refutation algorithms for SAT (or any other Boolean CSP) at similar clause densities. Our algorithms match the known sum-of-squares lower bounds due to Grigoriev and Schonebeck, up to logarithmic factors. Additionally, we extend our techniques to give new results for certifying upper bounds on the injective tensor norm of random tensors

Fichte and Hegel on Recognition

In this paper I provide an interpretation of Hegel’s account of ‘recognition’ (Anerkennung) in the 1802-3 System of Ethical Life as a critique of Fichte’s account of recognition in the 1796-7 Foundations of Natural Right. In the first three sections of the paper I argue that Fichte’s account of recognition in the domain of right is not concerned with recognition as a moral attitude. I then turn, in section four, to a discussion of Hegel’s critique and transformation of Fichte’s conception of recognition. Hegel’s transformation consists, I argue, in the claim that a comprehensive account of recognition in the domain of right must be concerned with recognition as a moral attitude

Less-is-more effects without the recognition heuristic

Inferences consistent with “recognition-based” decision-making may be drawn for various reasons other than recognition alone. We demonstrate that, for 2-alternative forced-choice decision tasks, less-is-more effects (reduced performance with additional learning) are not restricted to recognition-based inference but can also be seen in circumstances where inference is knowledge-based but item knowledge is limited. One reason why such effects may not be observed more widely is the dependence of the effect on specific values for the validity of recognition and knowledge cues. We show that both recognition and knowledge validity may vary as a function of the number of items recognized. The implications of these findings for the special nature of recognition information, and for the investigation of recognition-based inference, are discusse

A framework for forensic face recognition based on recognition performance calibrated for the quality of image pairs

Recently, it has been shown that performance of a face recognition system depends on the quality of both face images participating in the recognition process: the reference and the test image. In the context of forensic face recognition, this observation has two implications: a) the quality of the trace (extracted from CCTV footage) constrains the performance achievable using a particular face recognition system; b) the quality of the suspect reference set (to which the trace is matched against) can be judiciously chosen to approach optimal recognition performance under such a constraint. Motivated by these recent findings, we propose a framework for forensic face recognition that is based on calibrating the recognition performance for the quality of pairs of images. The application of this framework to several mock-up forensic cases, created entirely from the MultiPIE dataset, shows that optimal recognition performance, under such a constraint, can be achieved by matching the quality (pose, illumination, and, imaging device) of the reference set to that of the trace. This improvement in recognition performance helps reduce the rate of misleading interpretation of the evidence

Face recognition technologies for evidential evaluation of video traces

Human recognition from video traces is an important task in forensic investigations and evidence evaluations. Compared with other biometric traits, face is one of the most popularly used modalities for human recognition due to the fact that its collection is non-intrusive and requires less cooperation from the subjects. Moreover, face images taken at a long distance can still provide reasonable resolution, while most biometric modalities, such as iris and fingerprint, do not have this merit. In this chapter, we discuss automatic face recognition technologies for evidential evaluations of video traces. We first introduce the general concepts in both forensic and automatic face recognition , then analyse the difficulties in face recognition from videos . We summarise and categorise the approaches for handling different uncontrollable factors in difficult recognition conditions. Finally we discuss some challenges and trends in face recognition research in both forensics and biometrics . Given its merits tested in many deployed systems and great potential in other emerging applications, considerable research and development efforts are expected to be devoted in face recognition in the near future

Understanding the link between emotional recognition and awareness, therapy, and training : a thesis presented in partial fulfilment of the requirements for the degree of Doctorate in Clinical Psychology at Massey University, Manawatū, New Zealand

Therapy is an emotionally laden event, both for individuals seeking therapeutic intervention and the therapists who provide it. While the recognition of emotions in the general population has been a popular topic of research, very little research has been conducted into the emotional competencies, or more specifically, emotion recognition and awareness of therapists. In addition, there are few studies on the effectiveness of emotion recognition training for therapists’ emotional competencies, which is surprising given the innately emotional moments that clients and therapists experience during therapeutic work. This study aimed to address these gaps by investigating the association between emotional recognition, awareness, practice, and training. Fifty five therapists made up of clinical psychologists, counsellors, and a psychotherapist completed an online task that involved completion of a social-emotional orientated questionnaire and an emotion recognition task. Of these 55 participants, 26 completed an emotion recognition training before completing the same task again, two weeks later, while the remainder 29 participants were instructed to participate in no emotion recognition training. The results revealed that, compared to the no treatment condition, those who received emotion recognition training were more accurate in their recognition of emotions and also reported higher use of therapeutic emotional practice. Unexpectedly, participants who completed emotion recognition training reported less emotional awareness than the control group. Related to this, an inverse relationship was found between emotion recognition ability and self-reported emotional awareness, as well as the finding for some support for an inverse relationship between emotion recognition ability and self-reported use of emotional practice. There are two implications of this research; first, emotion recognition training increases therapists’ accuracy in emotion recognition, and second, therapists may need to be provided emotional practice feedback by an alternative form rather than through supervision or client outcome. This is due to an inverse relationship being found between participants’ actual and perceived emotional awareness. Therefore, future research into social-emotional practices and client outcomes will be advised to be considered. The limitations of the study and areas for future research are also discussed