Why would a behaviour effect one sex? After reading the article Regular sleeping hours really are good for children—if they are girls I started wondering what would be a good explanation for something such as sleep patterns have an affect on cognition, and specifically higher in girls?

And are their other examples where one sex is influenced at a higher rate?
When I first read the article you cited, which was actually just paraphrased from a magazine, I was hoping that the actual researchers would of come up with a hypothesis as to what would of caused this.  If you weren't able to find the actual study, all you have to do is just Google the author's name + their University/College and their page will come up with all the research they've ever done.  Academics love to do this.  And boom the actual study is here:
http://jech.bmj.com/content/early/2013/06/25/jech-2012-202024

But they never sought out to at least hypothesize why...which was disheartening.  Sometimes you can find a derivative work on the side there too, which may be trying to explain.  Doesn't look like it here.  Oh well.          

Back to your original questions though:


  What would be a good explanation for something such as sleep patterns have an affect on cognition, and specifically higher in girls?


Physiologically and as a general guess: hormones, the subtle differences in the ways that our brains are set up structurally as well as chemically, which could of all been set up by evolution.  The true answer is probably expressed as some sort of very subtle mechanism in the brain that we may not find for a very long time - and that mechanism has been put there by evolution.  We just don't know why yet.  I'm going to halfway guess down below though.


  And are their other examples where one sex is influenced at a higher rate?


I'm sure you can think of a few pretty general stereotypes that are likely true.  In general, girls are more influenced by emotion than guys are.  In general, guys are more influenced by logic than girls are.  I can cite this if you want, but I'm sure you can think of a million examples too.

Do you think that because this study involves cognition, a topic that is usually thought (or maybe just taught) to be independent of gender, that that is completely true?  Evolution would mold cognition just like anything else.  Cognition is a very vague word to use anyway since there are so many different tests to measure it and so many different sub types of cognition.  Admittedly the researcher did a pretty thorough job with her tests, but she didn't do all the tests out there.

As a hypothesis:  Females deal with certain types of stress differently than males do.  Evolutionarily, you could hypothesize a milleu of reasons as to why the "females that responded to this stressor this way usually survived" because of x, y, and/or z.

In this case, they may be more susceptible to disturbances in their sleep (causing stress) and thus handle that type of stress differently than males do.  The study of the underlying causes of stress for a man or a woman is actually a pretty huge field as they seem to believe (you'll see in my citations or the side citations next to them on pubmed.gov) that chronic stress = depression.  It is a widely researched topic because of this.

There is going to be some granularity to this though.  Can't make generalizations.

Here's an interesting study some researchers did that showed the males up:


  Sex differences associated with intermittent swim stress.
  Warner TA, Libman MK, Wooten KL, Drugan RC. Stress. 2013 Aug 12.
  Source Department of Psychology, University of New Hampshire, Durham, NH 03824, USA.     http://www.ncbi.nlm.nih.gov/pubmed/23930864
  
  Abstract
  Various animal models of depression have been used to seek a greater understanding of stress-related disorders. However, there is still a great need for novel research in this area, as many individuals suffering from depression are resistant to current treatment methods. Moreover, women gave a higher rate of depression, highlighting the need to investigate mechanisms of sex differences. Therefore, we employed a new animal model to assess symptoms of depression, known as intermittent swim stress (ISS). In this model, the animal experiences 100 trials of cold water swim stress. ISS has already been shown to cause signs of behavioral depression in males, but has yet to be assessed in females. Following ISS exposure, we looked at sex differences in the Morris water maze and forced swim test. The results indicated a spatial learning effect only in the hidden platform task between male and female controls, and stressed and control males. A consistent spatial memory effect was seen for males exposed to ISS. In the forced swim test, both sexes exposed to ISS exhibited greater immobility, and the same males and females also showed attenuated climbing and swimming, respectively. The sex differences could be due to different neural substrates for male and females. The goal of this study was to provide the first behavioral examination of sex differences following ISS exposure, so the stage of estrous cycle was not assessed for the females. This is a necessary future direction for subsequent experiments. The current paper highlights the importance of sex differences in response to stress, which may have bearing on disease mechanisms.
  PMID: 23930864 [PubMed - as supplied by publisher]


So, in that case the males got the blunt of it when having to go through that crazy course.  Their "spatial learning" was messed up in comparison to the female's - whose weren't - but just during one specific part of the course.

It's very granular, but still interesting nonetheless.

Here's another interesting one.  It actually seeks and does a pretty good job at explaining why females tend to overeat as a coping strategy for certain types of stress.  Actually one thing I don't like about this study is how it generalizes the word "stress" instead of the specific "stressor."  Regardless, it does quite a good and interesting job explaining the hormonal, physiological reasons why females overeat when they are "stressed" as the paper says.


  Gender differences in ghrelin response to chronic immobilization stress in
  rats: possible role of estrogen. Elbassuoni EA. Source Physiology
  Department, Minia University School of Medicine, Minia, Egypt.
  emanelbassuoni@yahoo.com. Gen Physiol Biophys. 2013 Aug 12.
  
  Abstract Ghrelin is a peptidergic hormone
  known to be one of the main hormones involved in the regulation of
  energy balance. Here we evaluated ghrelin response to stress in rats
  after ovariectomy and during estradiol benzoate (EB) therapy and
  compared results of males and females, to know whether ghrelin is
  involved in disordered eating behaviors in response to stress, and for
  understanding differences between males and females in food intake and
  weight gain especially during stress. 96 adult rats were classified
  into; male, female, ovariectomized (Ovx), Ovx with EB. Half animals of
  each group were exposed to immobilization stress 20 min/day for 21
  days. We found that chronic stress significantly augments serum
  ghrelin levels in both males and females, which is correlated with an
  increase in food intake and body weight. Females displayed significant
  higher ghrelin than males especially in response to stress,
  ovariectomy suppresses serum ghrelin in both unstressed and stressed
  females which is rescued by replacement with EB. EB replacement
  augments ghrelin response to stress in Ovx female, and reduces food
  intake and body weight. In conclusion, there is a clear sex difference
  in ghrelin secretion in response to stress caused by EB, since it
  amplifies ghrelin response to stress in females. PMID: 23940093
  [PubMed - as supplied by publisher]


Here is another really juicy and interesting one actually.  The abstract is long and translated from French, but I'm going to post and bold it to highlight more instances where X variable affects females more than males or vice versa. By the way, the article was written as this big block...I didn't write it this way.  As I began to bold things, they started making all these crazy assumptions which they actually end up proving most of.  The french went REALLY in depth here - at least psychologically.  So if you're interested in some psychological influencers and the differences between them in men and women this is for you:


  Girls are more successful than boys at the university. Gender group differences in models integrating motivational and aggressive
  components correlated with Test-Anxiety.  Masson AM, Hoyois P, Cadot
  M, Nahama V, Petit F, Ansseau M.  Service de Psychiatrie, Université
  de Liège, Belgique.  Encephale. 2004 Jan-Feb;30(1):1-15.
  Abstract
  It is surprising to note the evolution of success rates in Belgian
  universities especially in the first Year. Men are less successful
  than women and the differences are escalating in an alarming way.
  Dropouts take the same direction and women now represent a majority of
  the students at the university. In a previous study, we assessed 616
  students in the first Year at the university of Liège with Vasev, the
  English name of which was TASTE, a self report questionnaire
  constituted of 4 factors: anxiety, self confidence, procrastination
  and performance value; anxiety particularly concerned somatic
  expression of students before and during test evaluations; self
  confidence was a cognitive component close to self efficacy;
  procrastination was the behavioral component characterizing avoidance
  when students are confronted with the risk of failure; performance
  value referred to intrinsic and extrinsic motivations. French
  validation of TASTE led to an abbreviated version of 50 items (THEE)
  consisting of 5 factors, the four of TASTE and an additional one, very
  consistent, at first called depression because of its correlations
  with this dimension, then called sense of competence on account of its
  semantic content. Self-competence has been described in the literature
  of Achievement Motivation and corresponded to expectancy and ability
  beliefs in performance process which was also relevant to
  self-efficacy except the particularity of comparison with others,
  which was not included in the last construct. Self-competence has been
  considered as an important part of the Worry component of test
  anxiety. Some Authors didn't hesitate to view causality flowing from
  self-competence to test anxiety and have conceptualized the latter as
  a failure of the self where one's sense of competence has been
  undermined as a result of experienced failure. In our study, only that
  factor was equally scored in women and men whereas it was scored
  higher in failed students. In other respects anxiety and performance
  value were scored higher in women, *self-confidence and procrastination
  higher in men*. Because TASTE didn't discriminate the different
  components of motivation (performance value referred to intrinsic and
  extrinsic motivations without precise distinction) we decided to use
  the MPS (Multidimensional Perfectionism Scale) which gave the
  opportunity to distinguish SOP (Self Oriented Perfectionism) ie, the
  self-imposed unrealistic standards with inability to accept faults in
  order to know and master a subject, that corresponded to intrinsic
  motivation; SPP (Socially Prescribed Perfectionism) ie, the
  exaggerated expectancies of others which are subjectively believed as
  imposed and uncontrollable leading to anxiety, feelings of failure or
  helplessness, that corresponded to extrinsic motivation; POO
  (Perfectionism Oriented to Others) ie, the unrealistic demands
  expected from significant others, which especially characterized
  males. We assumed (I apologize for the assumptions they start making, lol) 
  submitted more to society exigencies.** That way extrinsic and intrinsic
  motivations were probably more combined unlike men who, dreading a
  loss of self esteem, tried to avoid failure responsibility in using
  self handicapping or aggressive behaviours, so separating motivation
  in an extrinsic part turned to performance value and an intrinsic one
  more concerned by self confidence and sense of competence with the
  result that the motivational balance was surely disrupted in case of
  high competition leading to failure or avoidance. 
  
  In another previous study we established a structural model illustrating, according to
  gender, correlations between anxiety, sense of incompetence,
  self-oriented perfectionism and socially prescribed perfectionism.
  Self-oriented perfectionism was less correlated to socially prescribed
  perfectionism in boys than in girls; furthermore especially by those
  who had never failed, it was negatively correlated to sense of
  incompetence, thus leading to lower scores of anxiety while in girls,
  by contrast, such a correlation didn't exist, thus involving higher
  anxiety. That way, on the one hand, intrinsic and extrinsic
  motivations by female students complementarily operated on the sense
  of incompetence and consequently on anxiety, the emotional component
  of test anxiety; on the other hand, by male students, intrinsic
  motivation had a negative correlation with the sense of incompetence
  and a lower correlation with extrinsic motivation, thereby shedding
  some light on the problem of anxiety level differences according to
  gender. More, that observation corresponded well to the model of
  self-worth where test anxiety was understood as a manifestation of
  perceived incompetence and as a defensive way to ward off negative
  self-evaluation; that model suited particularly well to boys and
  explained their attempts to maintain self-worth when risking academic
  failure. The present research assumes that independence or combination
  of motivation components is also correlated to different expressions
  of aggressiveness: hostility corresponding to threat and
  characterizing more girls while physical aggression is corresponding
  to personal challenge, a more masculine attribution. *If fighting
  against the sense of incompetence actually characterizes men and
  consequently shows too the competitive aspects of performance strong
  enough to mobilize intrinsic motivation, what would be expected
  regarding the notion of threat suspected to be predominant in girls?*
  The idea of using a questionnaire discriminating the specific
  dimensions of aggressiveness in fact the Aggression Questionnaire
  should meet the following purposes: At first establish a French
  version of that aggression questionnaire, perform the factorial
  analyses and internal consistency, compare them with other previous
  samples, then differentiate gender in general and in failure versus
  success situations. Finally include the different components of
  aggressiveness in the first described model and build a new one liable
  to define in boys the explicit pathways between test anxiety,
  perfectionism and aggressiveness. Statistical analyses have confirmed,
  in a 3 factor solution, the presence of emotional (anger), cognitive
  (hostility) and behavioural (physical aggression) components. Internal
  consistency is satisfactory. It is demonstrated that physical
  aggression characterizes boys (F=12.04, p=0.0001) while hostility
  (F=5.22, p=0.0015) and anger (F=0.49, p=0.0001) characterizes girls;
  furthermore it is noted that physical aggression characterizes more
  failed students (F=13.43, p=0.0003). Four models (see figures 2, 3, 4,
  5) have been established, at first focused on the distinction of
  correlations between motivation and cognitive and emotional components
  on the samples of boys (n=268) and girls (348), then developed on the
  samples of successful students, male (n=193) and female (n=271). They
  describe the differentiated action of intrinsic and extrinsic
  motivations on the different components of aggressiveness and
  test-anxiety according to gender and without experience of failure.
  The dynamic process of the organizational factors is different
  according to gender and psychopathology resulting from the
  combinations of behaviors, cognitions and emotions would be assumed,
  prioritizing physical aggression and psychopathy by boys, anxiety and
  depression by girls. Anyway more explanation about the evolution of
  success rates of boys and girls in Belgian universities is proposed.
  PMID: 15029071 [PubMed - indexed for MEDLINE]


I can't post anymore links cause I don't have enough rep, but if you go to pubmed.gov and search for the title of this article you'll see many many more related ones that I could just keep citing.  Anyways hope this helps, I gotta get some work done now, ha.

Alright here is more research:

I have the citation with what I feel is the most relevant sentance(s) in the abstract after scanning them.




  Luine V. Sex differences in chronic stress effects on memory in rats. Stress. 2002
  Sep;5(3):205-16. Department of Psychology, Hunter
  College of the City University of New York, NY 10021, USA.
  vluine@shiva.hunter.cuny.edu
  
  Relevant Sentance: "Given the same chronic stress--21 days of
  restraint for 6 h each day--males were impaired in all of the memory
  tests while females showed enhanced performance of the spatial memory
  tasks and no changes in object recognition performance."
  
  "recent studies show sexually differentiated cognitive responses to
  chronic stress and underline the importance of considering the
  sex/gender of subjects when studying the stress response."





  Bowman RE, Beck KD, Luine VN. Chronic stress effects on memory: sex
  differences in performance and monoaminergic activity.  Horm Behav.
  2003 Jan;43(1):48-59.  Department of Psychology, Hunter College of the
  City University of New York, 695 Park Avenue, New York, NY 10021, USA.
  bowmanr@sacredheart.edu   
  
  "stress differentially affected central transmitter levels in the
  frontal cortex, hippocampus, and amygdala depending on sex"





  Bowman RE, Micik R, Gautreaux C, Fernandez L, Luine VN.  Sex-dependent
  changes in anxiety, memory, and monoamines following one week of
  stress. Physiol Behav. 2009 Apr 20;97(1):21-9. doi:
  10.1016/j.physbeh.2009.01.012. Epub 2009 Jan 22.  Sacred Heart University, Fairfield, CT, United States. bowmanr@sacredheart.edu
  
  "these sexually dimorphic neurochemical changes following stress may
  underlie the behavioral differences. Current results show that
  short-term restraint elicits sex-dependent behavioral and neural
  changes different from those previously reported for longer term
  stresses and suggest that the temporal relationship between the change
  from adaptive to maladaptive responses to stress is shorter in male
  than female rats."


Now you could easily criticize me here and say I either got too many citations from Bowman RE (which I probably did) or that these are all based in rats...and...well...humans arn't rats.

I can find some more human studies that probably map MRI or something, but part of the value you lose is in that you, for instance, can't squirt them full of estrogen or take their ovaries out and say "try again" let's see how you do (feel free to edit that last part out as it kind of grossed me out too).  

Each way has it's own advantage/disadvantages.