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"Cameron, Alex"
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A recently quenched galaxy 700 million years after the Big Bang
Local and low-redshift (
z
< 3) galaxies are known to broadly follow a bimodal distribution: actively star-forming galaxies with relatively stable star-formation rates and passive systems. These two populations are connected by galaxies in relatively slow transition. By contrast, theory predicts that star formation was stochastic at early cosmic times and in low-mass systems
1
–
4
. These galaxies transitioned rapidly between starburst episodes and phases of suppressed star formation, potentially even causing temporary quiescence—so-called mini-quenching events
5
,
6
. However, the regime of star-formation burstiness is observationally highly unconstrained. Directly observing mini-quenched galaxies in the primordial Universe is therefore of utmost importance to constrain models of galaxy formation and transformation
7
,
8
. Early quenched galaxies have been identified out to redshift
z
< 5 (refs.
9
–
12
) and these are all found to be massive (
M
⋆
> 10
10
M
⊙
) and relatively old. Here we report a (mini-)quenched galaxy at
z
= 7.3, when the Universe was only 700 Myr old. The JWST/NIRSpec spectrum is very blue (
U
–
V
= 0.16 ± 0.03 mag) but exhibits a Balmer break and no nebular emission lines. The galaxy experienced a short starburst followed by rapid quenching; its stellar mass (4–6 × 10
8
M
⊙
) falls in a range that is sensitive to various feedback mechanisms, which can result in perhaps only temporary quenching.
Analysis of the JWST/NIRSpec spectrum of the recently observed Lyman-break galaxy JADES-GS+53.15508-27.80178 revealed a redshift of
z
= 7.3, a Balmer break and a complete absence of nebular emission lines, indicating that quenching occurred only 700 million years after the Big Bang.
Journal Article
Spectroscopic confirmation of two luminous galaxies at a redshift of 14
The first observations of the James Webb Space Telescope (JWST) have revolutionized our understanding of the Universe by identifying galaxies at redshift
z
≈ 13 (refs.
1
,
2
–
3
). In addition, the discovery of many luminous galaxies at Cosmic Dawn (
z
> 10) has suggested that galaxies developed rapidly, in apparent tension with many standard models
4
,
5
,
6
,
7
–
8
. However, most of these galaxies lack spectroscopic confirmation, so their distances and properties are uncertain. Here we present JWST Advanced Deep Extragalactic Survey–Near-Infrared Spectrograph spectroscopic confirmation of two luminous galaxies at
z
=
14.32
−
0.20
+
0.08
and
z
= 13.90 ± 0.17. The spectra reveal ultraviolet continua with prominent Lyman-α breaks but no detected emission lines. This discovery proves that luminous galaxies were already in place 300 million years after the Big Bang and are more common than what was expected before JWST. The most distant of the two galaxies is unexpectedly luminous and is spatially resolved with a radius of 260 parsecs. Considering also the very steep ultraviolet slope of the second galaxy, we conclude that both are dominated by stellar continuum emission, showing that the excess of luminous galaxies in the early Universe cannot be entirely explained by accretion onto black holes. Galaxy formation models will need to address the existence of such large and luminous galaxies so early in cosmic history.
JWST–NIRSpec spectroscopic confirmation of two luminous galaxies is presented, proving that luminous galaxies were already in place 300 million years after the Big Bang and are more common than what was expected before JWST.
Journal Article
Carbonaceous dust grains seen in the first billion years of cosmic time
Large dust reservoirs (up to approximately 10
8
M
⊙
) have been detected
1
–
3
in galaxies out to redshift
z
≃ 8, when the age of the Universe was only about 600 Myr. Generating substantial amounts of dust within such a short timescale has proven challenging for theories of dust formation
4
,
5
and has prompted the revision of the modelling of potential sites of dust production
6
–
8
, such as the atmospheres of asymptotic giant branch stars in low-metallicity environments, supernova ejecta and the accelerated growth of grains in the interstellar medium. However, degeneracies between different evolutionary pathways remain when the total dust mass of galaxies is the only available observable. Here we report observations of the 2,175 Å dust attenuation feature, which is well known in the Milky Way and galaxies at
z
≲ 3 (refs.
9
–
11
), in the near-infrared spectra of galaxies up to
z
≃ 7, corresponding to the first billion years of cosmic time. The relatively short timescale implied for the formation of carbonaceous grains giving rise to this feature
12
suggests a rapid production process, possibly in Wolf–Rayet stars or supernova ejecta.
An (ultraviolet) dust attenuation feature at 2,175 Å, attributed to carbonaceous dust grains in the Milky Way and nearby galaxies, also exists in galaxies up to a redshift of 7.
Journal Article
Spectroscopic confirmation of four metal-poor galaxies at z = 10.3–13.2
Finding and characterizing the first galaxies that illuminated the early universe at cosmic dawn is pivotal to understand the physical conditions and the processes that led to the formation of the first stars. In the first few months of operations, imaging from the James Webb Space Telescope (JWST) has been used to identify tens of candidates of galaxies at redshift (z) greater than 10, less than 450 million years after the Big Bang. However, none of such candidates has yet been confirmed spectroscopically, leaving open the possibility that they are actually low-redshift interlopers. Here we present spectroscopic confirmation and analysis of four galaxies unambiguously detected at redshift 10.3 ≤ z ≤ 13.2, previously selected from JWST Near Infrared Camera imaging. The spectra reveal that these primeval galaxies are metal poor, have masses on the order of about 107–108 solar masses and young ages. The damping wings that shape the continuum close to the Lyman edge provide constraints on the neutral hydrogen fraction of the intergalactic medium from normal star-forming galaxies. These findings demonstrate the rapid emergence of the first generations of galaxies at cosmic dawn.As part of the JWST Advanced Deep Extragalactic Survey (JADES), NIRSpec has spectroscopically confirmed four young and metal-poor galaxies at redshift 10.3–13.2, from an early epoch of galaxy formation.
Journal Article
New upper bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers
A
$(p,q)$
-colouring of a graph
$G$
is an edge-colouring of
$G$
which assigns at least
$q$
colours to each
$p$
-clique. The problem of determining the minimum number of colours,
$f(n,p,q)$
, needed to give a
$(p,q)$
-colouring of the complete graph
$K_n$
is a natural generalization of the well-known problem of identifying the diagonal Ramsey numbers
$r_k(p)$
. The best-known general upper bound on
$f(n,p,q)$
was given by Erdős and Gyárfás in 1997 using a probabilistic argument. Since then, improved bounds in the cases where
$p=q$
have been obtained only for
$p\\in \\{4,5\\}$
, each of which was proved by giving a deterministic construction which combined a
$(p,p-1)$
-colouring using few colours with an algebraic colouring.
In this paper, we provide a framework for proving new upper bounds on
$f(n,p,p)$
in the style of these earlier constructions. We characterize all colourings of
$p$
-cliques with
$p-1$
colours which can appear in our modified version of the
$(p,p-1)$
-colouring of Conlon, Fox, Lee, and Sudakov. This allows us to greatly reduce the amount of case-checking required in identifying
$(p,p)$
-colourings, which would otherwise make this problem intractable for large values of
$p$
. In addition, we generalize our algebraic colouring from the
$p=5$
setting and use this to give improved upper bounds on
$f(n,6,6)$
and
$f(n,8,8)$
.
Journal Article
A (5,5)-Colouring of Kn with Few Colours
For fixed integers p and q, let f(n,p,q) denote the minimum number of colours needed to colour all of the edges of the complete graph Kn such that no clique of p vertices spans fewer than q distinct colours. Any edge-colouring with this property is known as a (p,q)-colouring. We construct an explicit (5,5)-colouring that shows that f(n,5,5) ≤ n1/3 + o(1) as n → ∞. This improves upon the best known probabilistic upper bound of O(n1/2) given by Erdős and Gyárfás, and comes close to matching the best known lower bound Ω(n1/3).
Journal Article
A (5,5)-Colouring of K n with Few Colours
For fixed integers
p
and
q
, let
f
(
n
,
p
,
q
) denote the minimum number of colours needed to colour all of the edges of the complete graph
K
n
such that no clique of
p
vertices spans fewer than
q
distinct colours. Any edge-colouring with this property is known as a (
p
,
q
)-colouring. We construct an explicit (5,5)-colouring that shows that
f
(
n
,5,5) ≤
n
1/3 +
o
(1)
as
n
→ ∞. This improves upon the best known probabilistic upper bound of
O
(
n
1/2
) given by Erdős and Gyárfás, and comes close to matching the best known lower bound Ω(
n
1/3
).
Journal Article
Power without Law
In Power without Law Alex Cameron enlivens the debate over judicial activism with an unprecedented examination of the details of the Marshall case, analyzing the evidence and procedure in the trial court and tracing the legal arguments through the Court of Appeal to the Supreme Court of Canada. He argues that there were critical defects in the process - the successful argument at the Supreme Court of Canada was never tested in the lower courts, the Crown's expert was precluded from testifying about a vital document, the Court's analysis does not accord with the historical evidence, and the treaty rights are inconsistent with the colonial law of Nova Scotia.
eBook
Collaborative Leadership, 2nd Edition
We all live in an interconnected world and for business leaders the last decade has seen a dramatic rise in the speed and scale of this interdependence. But while increased connectivity is inevitable, increased collaboration is not. To succeed in today’s environment, leaders need to be able to build relationships, handle conflict and to share control in order to promote effective collaboration where it is needed most.Archer and Cameron have been working in this field for over 10 years and were amongst the first business authors to define and explain Collaborative Leadership in their 2008 book. This 2nd edition draws on interviews, examples and additional cases studies of the new collaboration challenges that leaders face such as; working together to deal with the consequences of financial contagion in the Eurozone or elsewhere, responding to the growth in use of social networks by their staff and customers, and managing global supply chains to reach new growth markets.This fully revised, updated and re-structured text provides an easily accessible ‘how-to’ guide for leaders in today’s interconnected world. It will give both experienced and aspiring leaders the techniques and confidence to manage complex collaborative relationships in a sustainable way. It also acts as a guide for leadership development professionals, coaches and consultants who have to build leadership and collaboration capability within organizations.
eBook