Publications

Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past hundred years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRFT to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRFT. From these discussions, we can clearly state the FRFT is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the its digital realizations and applications, especially, since many digital realizations of the FRFT still lack properties of the continuous FRFT. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRFT offers many advantages over the traditional Fourier analysis.

Is visual attention required for visual consciousness? In the past decade, many have claimed that awareness can arise in the absence of attention. This claim is largely based on the notion that natural scene (or �gist�) perception occurs without attention. Against this, we first show that when observers perform a variety of demanding, sustained attention tasks, inattentional blindness occurs for natural scenes. In addition, scene perception is impaired under dual-task conditions, but only when using sufficiently demanding tasks. This suggests that previous studies claiming to have demonstrated scene perception without attention failed to fully engage attention and that natural scene perception does indeed require attention. Thus, natural scene perception is not a �preattentive� process and cannot be used to support the idea of awareness without attention.

This paper argues that obscure Homeric adjective ἀάατος is related to PIE *séh2u̯l̥, gen. sg. *sh2u̯éns ‘sun’ and goes back to a proto-form *ahāu̯ato- < *n̥seh2u̯n̥to- ‘not having sun’: the juncture ἀάατον Στυγὸς ὕδωρ (Ξ 271) can now be understood as ‘the sunless water of the Styx’. In the post-Homeric period this epithet underwent a formal renewal and is indirectly continued by ἀνάλιος / ἀνήλιος in tragedy (e.g. ἀνάλιον χέρσον (scil. of the Underworld) A. Th. 859). Under this analysis ἀάατο- < *ahāu̯ato- is best seen as an Aeolic element in the Homeric diction (which would also explain the absence of spiritus asper). While it is possible that *(a)hāu̯a to- ‘(not) having sun’ is a Proto-Greek coinage, formed from *hāu̯əl, oblique stem *hāu̯a(t)-, an expectable remodeling product of heteroclitic *séh2u̯l̥, *sh2u̯éns on the way to Greek, such athematic formation is not attested in Greek. This paper therefore argues for a possessive compound *(n̥-)seh2u̯n̥to- ‘not having sun(light)’ whose second member is a substantive *séh2u̯n̥to- ‘sunlight’ derived from adjectival *sh2un tó- ‘having sun’ by a substantivization process that involved an insertion of a new full-grade in the root in addition to the accent shift. Adj. *sh2un tó- is reflected both by Tocharian B swāñco, A swāñceṃ ‘sunbeam’ and by Proto-Germanic *sunþa ‘south’ ( < *súh2nto-, with a secondary substantivizing accent shift). The poetic status of reconstructed *n̥séh2u̯n̥to- in Indo-European is confirmed by the existence of similar formations derived from the word for ‘sun’ in archaic Indo-Iranian texts. This paper first discusses Vedic asū́rta- (RV X, 82, 4c): asū́rtam rájas- is the Vedic term for the Underworld, exactly matching the description of the Underworld river Styx as ἀάατος (rájas- = Ἔρεβος). Secondly, it is shown that YAvestan axvarəta-, the standing epithet of xvarənah-, can be traced back to a reconstruction *n̥-s(h2)u̯el to- and interpreted as ‘not lit by the sun’, which is exactly true of xvarənah-, concealed in the waters of the sea Vourukasəm (Yt. 19, 51-59). Lastly, no less significant is another YAvestan epithet xvanuuant- ‘sunny’, associated with the heavenly waters (Y. 16, 7) and one’s immortal life: xvahe gaiiehe xvanuuatō aməṣ̌ahe (Y. 9, 1; Yt. 8, 11). Thus, in a number of Indo-European traditions there is a close association between the sun, waters, and immortality. This study of several obscure and archaic epithets from three Indo-European poetic traditions makes it possible to suggest a new interpretation of a difficult Homeric word and reveals a further aspect of Indo-European poetics.

We marshal discoveries about human behavior and learning from social science research and show how they can be used to improve teaching and learning. The discoveries are easily stated as three social science generalizations: (1) social connections motivate, (2) teaching teaches the teacher, and (3) instant feedback improves learning. We show how to apply these generalizations via innovations in modern information technology inside, outside, and across university classrooms. We also give concrete examples of these ideas from innovations we have experimented with in our own teaching. See also a video presentation of this talk before the Harvard Board of Overseers

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