Boolean approximate counting CSPs with weak conservativity, and implications for ferromagnetic two-spin

We analyse the complexity of approximate counting constraint satisfactions problems #CSP(F), where F is a set of nonnegative rational-valued functions of Boolean variables. A complete classification is known if F contains arbitrary unary functions. We strengthen this result by fixing any permissive strictly increasing unary function and any permissive strictly decreasing unary function, and requiring only those to be in F. The resulting classification is employed to characterise the complexity of a wide range of two-spin problems, fully classifying the ferromagnetic case. Furthermore, we also consider what happens if only the pinning functions are assumed to be in F. We show that any set of functions for which pinning is not sufficient to recover the two kinds of permissive unaries must either have a very simple range, or must satisfy a certain monotonicity condition. We exhibit a non-trivial example of a set of functions satisfying the monotonicity condition

Matrix Calculus for Classical and Quantum Circuits

Quantum computation on w qubits is represented by the infinite unitary group U(2^w); classical reversible computation on w bits is represented by the finite symmetric group S_{2^w}. In order to establish the relationship between classical reversible computing and quantum computing, we introduce two Lie subgroups~XU(n) and~ZU(n) of the unitary group~U(n). The former consists of all unitary $n \times n$ matrices with all line sums equal to 1; the latter consists of all unitary diagonal n X n matrices with first entry equal to 1. Such group structure also reveals the relationship between matrix calculus and diagrammatic zx-calculus of quantum circuits

Influence of DGKH variants on amygdala volume in patients with bipolar affective disorder and schizophrenia

The diacylglycerol kinase eta (DGKH) gene, first identified in a genome-wide association study, is one of the few replicated risk genes of bipolar affective disorder (BD). Following initial positive studies, it not only was found to be associated with BD but also implicated in the etiology of other psychiatric disorders featuring affective symptoms, rendering DGKH a cross-disorder risk gene. However, the (patho-)physiological role of the encoded enzyme is still elusive. In the present study, we investigated primarily the influence of a risk haplotype on amygdala volume in patients suffering from schizophrenia or BD as well as healthy controls and four single nucleotide polymorphisms conveying risk. There was a significant association of the DGKH risk haplotype with increased amygdala volume in BD, but not in schizophrenia or healthy controls. These findings add to the notion of a role of DGKH in the pathogenesis of BD.DFG [RTG 1253/1, RE1632/5-1]; BMBF (DZHI) [01EO1004]; IZKF [Z3-24