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The SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) is a three-year JCMT Large Program aiming at reaching the 450 \\(\\mu\\)m confusion limit in the COSMOS-CANDELS region, to study a representative sample of the high-redshift far-infrared galaxy population that gives rise to the bulk of the far-infrared background. We present the first-year data from STUDIES. We have reached a 450 \\(\\mu\\)m noise level of 0.91~mJy for point sources at the map center, covered an area of 151 arcmin\\(^2\\), and detected 98 and 141 sources at 4.0 and 3.5 \\(\\sigma\\), respectively. Our derived counts are best constrained in the 3.5-25 mJy regime using directly detected sources. Below the detection limits, our fluctuation analysis further constrains the slope of the counts down to 1 mJy. The resulting counts at 1-25 mJy are consistent with a power law having a slope of \\(-2.59\\) (\\(\\pm0.10\\) for 3.5-25 mJy, and \\(^{+0.4}_{-0.7}\\) for 1-3.5 mJy). There is no evidence of a faint-end termination or turn-over of the counts in this flux density range. Our counts are also consistent with previous SCUBA-2 blank-field and lensing cluster surveys. The integrated surface brightness from our counts down to 1 mJy is \\(90.0\\pm17.2\\) Jy deg\\(^{-2}\\), which can account for up to \\(83^{+15}_{-16}\\%\\) of the COBE 450 \\(\\mu\\)m background. We show that Herschel counts at 350 and 500 \\(\\mu\\)m are significantly higher than our 450 \\(\\mu\\)m counts, likely caused by its large beam and source clustering. High-angular resolution instruments like SCUBA-2 at 450 \\(\\mu\\)m are therefore highly beneficial for measuring the luminosity and spatial density of high-redshift dusty galaxies.

Variability detected in galaxies is usually attributed to their active galactic nuclei (AGNs). While all AGNs are intrinsically variable, the AGN unification model predicts that type~2 AGNs rarely vary because their engines are blocked by dust tori. Previous UV-to-near-IR variability studies largely support this expectation. Here, we present a variability study by James Webb Space Telescope (JWST) that reveals a more subtle picture. Using NIRCam imaging data from three surveys over \\(\\)140~arcmin\\(^2\\) in the COSMOS field, we found 117 galaxies with$\\geq 4$ $\\sigma\\( variability in the F356W band across \\)\\sim\\(2-year baseline. Cross-matching with the existing JWST spectroscopic data, we identified five of them at \\)z=0.19\\(--3.69 (F356W corresponding to rest-frame \\)\\lambda\\approx0.76-2.97\\(~\\)\\mu\\(m), which were all coincidentally observed by a NIRSpec program almost contemporaneously with the last imaging epoch. One additional variable was identified at \\)z=0.90\\( using the archival Keck telescope data. These six objects form our spectroscopic subsample. Interestingly, two reside in close-pair environments, while two others form a close pair themselves. Most of their light curves can hardly be explained by nuclear transients, and AGN variability is a more plausible cause. However, among these six objects, (1) only one shows broad Bracket and Pfund series permitted lines (\\)\\Delta v > 1000\\(~km~s\\)^{-1}\\() indicative of a type~1 AGN; (2) two show narrow permitted lines (H\\)\\alpha\\( and/or He~I\\)\\lambda10830$ ) consistent with type~2 AGNs, with another one likely type~2 based on the host galaxy properties; and (3) two others, which form a pair, show no emission lines. Our results add more challenges to the unification model.

Variability detected in galaxies is usually attributed to their active galactic nuclei (AGNs). While all AGNs are intrinsically variable, the classic AGN unification model predicts that type~2 AGNs rarely vary because their engines are obstructed by dust tori. Previous UV-to-near-IR variability studies largely support this expectation. Here, we present a variability study by James Webb Space Telescope (JWST) that reveals a more subtle picture. Using NIRCam imaging data from three surveys over \\(\\sim\\)140~arcmin\\(^2\\) in the COSMOS field, we found 117 galaxies with $\\geq 4$$\\sigma\\( variability in the F356W band across a \\)\\sim\\(2-year baseline. Cross-matching with existing JWST spectroscopic data in this area, we identified five of them at \\)z=0.19\\(--3.69, which were all coincidentally observed by a NIRSpec program almost contemporaneously with the last imaging epoch. One additional variable was identified at \\)z=0.90\\( using the archival Keck telescope data. These six objects form our spectroscopic subsample. Interestingly, two reside in close-pair environments, while two others form a close pair themselves. Most of their light curves can hardly be explained by nuclear transients, and AGN variability is a more plausible cause. However, among these six objects, (1) only one shows broad permitted lines (\\)\\Delta v > 1000\\(~km~s\\)^{-1}$) indicative of a type~1 AGN; (2) two show narrow permitted lines consistent with type~2 AGNs, with another one likely type~2 based on the host galaxy properties; and (3) two others, which form a pair, show no emission lines. Our results add more challenges to the unification model.

Variability is a fundamental signature for active galactic nuclei (AGN) activity, and serve as an unbiased indicator for rapid instability happened near the center supermassive black hole (BH). Previous studies showed that AGN variability does not have strong redshift evolution, and scales with their bolometric luminosity and BH mass, making it a powerful probe to identify low-mass, low-luminosity AGNs at high redshift. JWST has discovered a new population of high-redshift galaxies likely hosting moderate accreting BHs (\\(10^6\\,M_\\odot\\)) -- the little red dots (LRDs, \\(z=4-10\\)). In this paper, we study the variability of a sample of 21 LRDs with V-shaped SEDs in three JWST deep fields that also have reliable HST observations in closely paired filters at 1-2 um (rest-frame UV), with the time difference between 6 and 11 years. This LRD sample covers a redshift range of \\(3

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