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Depression--be it a formal diagnosis based on consensus clinical criteria, or a collection of symptoms revealed by a self-report rating scale--is common in patients with multiple sclerosis (MS) and adds substantially to the morbidity and mortality associated with this disease. This Review discusses the prevalence and epidemiology of depression in patients with MS, before covering aetiological factors, including genetics, brain pathology, immunological changes, dysregulation of the hypothalamic-pituitary-adrenal axis, and psychosocial influences. Treatment options such as antidepressant drugs, cognitive-behavioural therapy, mindfulness-based therapy, exercise and electroconvulsive therapy are also reviewed in the context of MS-related depression. Frequent comorbid conditions, namely pain, fatigue, anxiety, cognitive dysfunction and alcohol use, are also summarized. The article then explores three key challenges facing researchers and clinicians: what is the optimal way to define depression in the context of diseases such as MS, in which the psychiatric and neurological symptoms overlap; how can current knowledge about the biological and psychological underpinnings of MS-related depression be used to boost the validity of this construct; and can intervention be made more effective through use of combination therapies with additive or synergistic effects, which might exceed the modest benefits derived from their individual components?

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We study the Potts model (defined geometrically in the cluster picture) on finite two-dimensional lattices of size L×N , with boundary conditions that are free in the L-direction and periodic in the N -direction. The decomposition of the partition function in terms of the characters K 1+2l (with l = 0, 1, . . . , L) has previously been studied using various approaches (quantum groups, combinatorics, transfer matrices). We first show that the K 1+2l thus defined actually coincide, and can be written as traces of suitable transfer matrices in the cluster picture. We then proceed to similarly decompose constrained partition functions in which exactly j clusters are non-contractible with respect to the periodic lattice direction, and a partition function with fixed transverse boundary conditions.