Over the past quarter century, the definition of entanglement has been extended, from information theory, to include mixed states
that are separable when given as combination of products of subsystem states.
The master equation describes the time evolution of mixed states
. For the rest of this paper we fix a stochastic reaction network (S, K, T, s, t, r).
Their topics include elementary convex analysis, quantum mechanics, for mathematicians, metric entropy and concentration of measure in classical spaces, Gaussian processes and random matrices, the geometry of the set of mixed states
, and Bell inequalities and the Grothendieck-Tsirelson inequality.
(2) Patients often present with mixed states
, such as manic or hypomanic states with mixed depressive features or a major depressive episode combined with subsyndromal hypomania or mania.
Usually one regards mixed states
as representing one's state of knowledge of, in this example, the quantum coin.
This return to thinking of mood disorders as existing on a continuum, as psychiatrist Emil Kraepelin, MD, theorized around the turn of the last century, pivots on the decision to do away with mixed states
and to instead add the mixed features specifier.
They began after World War I, when the former Ottoman Empire was carved into ethnically and religiously mixed states
We consider a provision to be associated with less identity theft if it is common in the Better states, uncommon in the Worse states, and neither common nor uncommon in Mixed states
. For example, in the 2006-09 period, 81.3 percent of states in the Better group had the State Enforcement provision compared with 67.1 percent of states in the Mixed group and 51.7 percent of states in the Worse group, suggesting the State Enforcement provision is associated with lower identity theft (Table 4).
As Bosnia, Syria and Iraq have shown, divorces in mixed states
invariably lead to great violence as every community tries to carve out a "pure" territory for itself.
In some patients, treatment with antidepressant medication precipitates the emergence of mixed states
.  In patients with MDD, the presence of co-occurring manic symptoms has been associated with an increased risk of suicidal behavior,  more depressive episodes,  poorer response to treatment,  more atypical features of depression,  younger age of onset,  and increased familial risk of bipolar disorder.
In the instance of mixed states
, a particularly convenient measure for two-qubit systems is the concurrence C([rho]) [43, 44].
A BD diagnosis is highly predicted by mixed states
, especially BD II, which has been linked with an increased lifetime risk for comorbid psychiatric disorders, more mood episodes, higher rates of treatment contacts, and lower rates of full-time employment compared to pure states.