Balanced triangulations on few vertices and an implementation of cross-fips

A d -dimensional simplicial complex is balanced if the underlying graph is ( d + 1 ) -colorable. We present an implementation of cross-flips, a set of local moves introduced by Izmestiev, Klee and Novik which connect any two PL-homeomorphic balanced combinatorial manifolds. As a result we exhibit a vertex minimal balanced triangulation of the real projective plane, of the dunce hat and of the real projective space, as well as several balanced triangulations of surfaces and 3-manifolds on few vertices. In particular we construct small balanced triangulations of the 3-sphere that are non-shellable and shellable but not vertex decomposable

Graded Betti Numbers of Balanced Simplicial Complexes

We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings S/I, where S is a polynomial ring and I subset of S is a homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner rings of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type

A balanced non-partitionable cohen-macaulay complex

In a recent article, Duval, Goeckner, Klivans and Martin disproved the longstanding conjecture by Stanley, that every Cohen–Macaulay simplicial complex is partitionable. We construct counterexamples to this conjecture that are even balanced, i.e. their underlying graph has a minimal coloring. This answers a question by Duval et al. in the negative

Main clinical features in patients at their first psychiatric admission to Italian acute hospital psychiatric wards. The PERSEO study

BACKGROUND: Few data are available on subjects presenting to acute wards for the first time with psychotic symptoms. The aims of this paper are (i) to describe the epidemiological and clinical characteristics of patients at their first psychiatric admission (FPA), including socio-demographic features, risk factors, life habits, modalities of onset, psychiatric diagnoses and treatments before admission; (ii) to assess the aggressive behavior and the clinical management of FPA patients in Italian acute hospital psychiatric wards, called SPDCs (Servizio Psichiatrico Diagnosi e Cura = psychiatric service for diagnosis and management). METHOD: Cross-sectional observational multi-center study involving 62 Italian SPDCs (PERSEO – Psychiatric EmeRgency Study and EpidemiOlogy). RESULTS: 253 FPA aged <= 40 were identified among 2521 patients admitted to Italian SPDCs over the 5-month study period. About half of FPA patients showed an aggressive behavior as defined by a Modified Overt Aggression Scale (MOAS) score greater than 0 Vs 46% of non-FPA patients (p = 0.3651). The most common was verbal aggression, while about 20% of FPA patients actually engaged in physical aggression against other people. 74% of FPA patients had no diagnosis at admission, while 40% had received a previous psychopharmacological treatment, mainly benzodiazepines and antidepressants. During SPDC stay, diagnosis was established in 96% of FPA patients and a pharmacological therapy was prescribed to 95% of them, mainly benzodiazepines, antipsychotics and mood stabilizers. CONCLUSION: Subjects presenting at their first psychiatric ward admission have often not undergone previous adequate psychiatric assessment and diagnostic procedures. The first hospital admission allows diagnosis and psychopharmacological treatment to be established. In our population, aggressive behaviors were rather frequent, although most commonly verbal. Psychiatric symptoms, as evaluated by psychiatrists and patients, improved significantly from admission to discharge both for FPA and non-FPA patients

Clinical features and therapeutic management of patients admitted to Italian acute hospital psychiatric units: the PERSEO (psychiatric emergency study and epidemiology) survey

<p>Abstract</p> <p>Background</p> <p>The PERSEO study (psychiatric emergency study and epidemiology) is a naturalistic, observational clinical survey in Italian acute hospital psychiatric units, called SPDCs (Servizio Psichiatrico Diagnosi e Cura; in English, the psychiatric service for diagnosis and management). The aims of this paper are: (i) to describe the epidemiological and clinical characteristics of patients, including sociodemographic features, risk factors, life habits and psychiatric diagnoses; and (ii) to assess the clinical management, subjective wellbeing and attitudes toward medications.</p> <p>Methods</p> <p>A total of 62 SPDCs distributed throughout Italy participated in the study and 2521 patients were enrolled over the 5-month study period.</p> <p>Results</p> <p>Almost half of patients (46%) showed an aggressive behaviour at admission to ward, but they engaged more commonly in verbal aggression (38%), than in aggression toward other people (20%). A total of 78% of patients had a psychiatric diagnosis at admission, most frequently schizophrenia (36%), followed by depression (16%) and personality disorders (14%), and no relevant changes in the diagnoses pattern were observed during hospital stay. Benzodiazepines were the most commonly prescribed drugs, regardless of diagnosis, at all time points. Overall, up to 83% of patients were treated with neuroleptic drugs and up to 27% received more than one neuroleptic either during hospital stay or at discharge. Atypical and conventional antipsychotics were equally prescribed for schizophrenia (59 vs 65% during stay and 59 vs 60% at discharge), while atypical drugs were preferred in schizoaffective psychoses (72 vs 49% during stay and 70 vs 46% at discharge) and depression (41 vs 32% during stay and 44 vs 25% at discharge). Atypical neuroleptics were slightly preferred to conventional ones at hospital discharge (52 vs 44%). Polypharmacy was in general widely used. Patient attitudes toward medications were on average positive and self-reported compliance increased during hospital stay.</p> <p>Conclusion</p> <p>Results confirm the widespread use of antipsychotics and the increasing trend in atypical drugs prescription, in both psychiatric in- and outpatients.</p

Minimality of tensors of fixed multilinear rank

We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of the fixed multilinear rank form a minimal submanifold of the Euclidean space of tensors endowed with the Frobenius inner product. We also establish the absence of local extrema for linear functionals restricted to the submanifold of rank-one tensors, finding application in statistics

Spectral theory of weighted hypergraphs via tensors

One way to study a hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper, we study how properties of weighted hypergraphs are reflected on eigenvalues and eigenvectors of their associated tensors. We also show how to efficiently compute eigenvalues with some techniques from numerical algebraic geometry