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This work studies the Clifford algebra approach to the density matrix. We discuss elementary examples of pure and mixed states by writing the density matrix as an element of the Clifford algebra of the three-dimensional space C l 3 . We also revisit the phenomenon of Larmor precession within the framework of Clifford algebra. Additionally, we discuss the geometrical interpretation of the so-called Clifford Density Element (CDE) for pure states in analogy to the Bloch sphere of conventional quantum theory. Finally, we discuss the dynamics of the CDE, which obeys an algebraic form of the Liouville von–Neumann equation. [ABSTRACT FROM AUTHOR]

The presence of noise affects the process of quantum computing and quantum communication, and quantum autoencoders (QAEs) provide a new solution for dealing with this problem. Previous study has shown that QAEs could denoise pure quantum states subject to spin-flip errors and random unitary noise (Bondarenko and Feldmann Phys Rev Lett 124: 130502, 2020). However, avoiding or reducing the interference of noise on mixed states remains an interesting problem in quantum communication and quantum computing. In this paper, the denoising effect of QAEs for mixed states is studied. We investigate the denoising effect of QAEs for a specific type of mixed states in four types of noise usually encountered in the real world, i.e., the bit-flip, the phase-flip, the depolarizing, and the amplitude-damping noise. Simulation results show that the QAEs can significantly denoise four types of noise on mixed states with different noisy and mixed parameters. [ABSTRACT FROM AUTHOR]

Mixed depressive states are defined by the co-presence of depressive and manic symptoms. They represent extremely variable conditions from the point of view of clinical expressiveness and are difficult to recognize, ranging from clear schizophrenic-like psychoses and pseudodemented pictures to subsyndromal psychopathology. At the basis of the extreme variability of depressive pictures with mixed features are the different combinations that depressive and manic symptoms can assume. Furthermore, the intensity of depressive symptoms and manic symptoms, combined, can be variable, a factor that contributes to making the picture even more variable. Each form of mixed depressive state therefore presents its own specific symptomatic characteristics and specific difficulties in differential diagnosis and each form requires a different therapeutic strategy. In this work we have distinguished four possible specific subtypes of mixed depressive states, describing their specific clinical presentation and the therapeutic options most supported by the literature with the aim of contributing to a better recognition of mixed depressive states, to avoid incorrect diagnoses at patient and treatments that are useless if not worsening. [ABSTRACT FROM AUTHOR]

This work presents a brief review on the modern approaches to data modeling by the methods developed in the quantum physics during the last one hundred years. Quantum computers and computations have already been widely investigated theoretically and attempted in some practical implementations, but methods of quantum data modeling are not yet sufficiently established. A vast range of concepts and methods of quantum mechanics have been tried in many fields of information and behavior sciences, including communications and artificial intelligence, cognition and decision making, sociology and psychology, biology and economics, financial and political studies. The application of quantum methods in areas other than physics is called the quantum-like paradigm, meaning that such approaches may not be related to the physical processes but rather correspond to data modeling by the methods designed for operating in conditions of uncertainty. This review aims to attract attention to the possibilities of these methods of data modeling that can enrich theoretical consideration and be useful for practical purposes in various sciences and applications.

We address a general question whether geometry of submanifolds of an integral compact Kähler manifold is characterized by invariants that come from analysis. In geometric quantization, we have an integral compact Kähler manifold M and a holomorphic line bundle L on this manifold. There is a known procedure how to associate a sequence of mixed states (ρ N) , N = 1 , 2 , 3 , ... , to a submanifold Λ of M. Do analytic properties of this sequence reflect the geometry of Λ ? In this paper, we consider the case when M is a product of two integral compact Kähler manifolds. We show that, when Λ is a product submanifold of M, then the entanglement of formation of ρ N is zero for all sufficiently large N. [ABSTRACT FROM AUTHOR]

This work presents a brief review on the modern approaches to data modeling by the methods developed in the quantum physics during the last one hundred years. Quantum computers and computations have already been widely investigated theoretically and attempted in some practical implementations, but methods of quantum data modeling are not yet sufficiently established. A vast range of concepts and methods of quantum mechanics have been tried in many fields of information and behavior sciences, including communications and artificial intelligence, cognition and decision making, sociology and psychology, biology and economics, financial and political studies. The application of quantum methods in areas other than physics is called the quantum-like paradigm, meaning that such approaches may not be related to the physical processes but rather correspond to data modeling by the methods designed for operating in conditions of uncertainty. This review aims to attract attention to the possibilities of these methods of data modeling that can enrich theoretical consideration and be useful for practical purposes in various sciences and applications. [ABSTRACT FROM AUTHOR]

Inspired by the recent experimental realization of topological transitions in circuit quantum electrodynamics and the research interest in the generalization of mixed states of topological geometric phases, we propose a scheme for probing topological phase transitions at finite temperature, which consists of two transmon qubits. Measurements of the mixed geometry phase shift, i.e. 2 π -discontinuous Uhlmann phase jumps, can verify the Uhlmann number of the simulated mixed state. By adjusting the systematic parameters, we are able to engineer a topological transition n U = 1 → 0 at finite temperature before allowing the degeneracy in the Hamiltonian to pass from inside to the outside of the manifold. According to our estimates based on conservative experimental parameters, the measurements are experimentally solvable. [ABSTRACT FROM AUTHOR]

Abstract This article introduces the concept proposed by the eminent second‐generation Japanese psychopathologist Tadao Miyamoto in 1992 that the manic‐depressive mixed state is the basic psychopathology of manic‐depressive illness. When Kraepelin first established the dichotomy between schizophrenia and manic‐depressive illness, mania and depression were placed in a symmetrical relationship. Now, in Diagnostic and Statistical Manual of Mental Disorders, 5th edition (DSM‐5), manic‐depressive illness is divided into two distinct categories: bipolar and related disorders, and depressive disorders. Miyamoto pointed out that even in the average depressed state there is a manic‐depressive mixed state and listed the following findings. The depressed mood of depression is itself a major fluctuation, but is constantly subject to more or less subtle fluctuations or swaying. What occurs in association with the incessant fluctuations of mood dysphoria are restlessness, agitation, irritability, and excitement, which manifest in a unique way in combination with a depressive mood. In depressive delusions, ideations of belittlement are developed in an exaggerated manner. Miyamoto concluded that mixed states are not incidental or accessory to manic‐depressive illness; on the contrary, they may form a core component of manic‐depressive illness.

In this note, we first derive a Schödinger uncertainty relation for any pair of quaternionic observables and a mixed state. Then, the Wigner–Yanase skew information is introduced in the quaternion setting. Based on the skew information, we establish a new quantum uncertainty inequality for the non-Hermitian quaternionic observables. [ABSTRACT FROM AUTHOR]

Quantum information encoded in an arbitrary quantum state can be hidden from the reduced subsystem and spread over quantum correlation, which is quantum information masking. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively from different perspectives. Firstly, for the masking quantum information encoded in pure states, we expand the maskable non-orthogonal set Q over previous literature. Then, for the masking quantum information encoded in mixed states, we acquire the restricted condition that the information contained in states ρ is masked by the operator S. Finally, we get a signification conclusion by working out a classification on S | 0 ⟩ and S | 1 ⟩ mapping result of masking quantum information encoded in mixed states. [ABSTRACT FROM AUTHOR]

The violation of Bell’s inequality in quantum mechanics implies that there exist nonlocality and entanglement. When the density matrix of a composite system cannot be written as a convex combination of the product of the density matrices of its subsystems, we say there exists entanglement. For pure states, the existence of entanglement always leads to the violation of Bell’s inequality. However, in the case of the mixed states, there may be entanglement, but Bell's inequality is not violated and in other words, the nonlocality is not manifested. In addition to Bell's inequality, quantum teleportation is also a manifestation of nonlocality. Quantum teleportation using entangled states is more successful than quantum teleportation with separable states. Therefore, the corresponding fidelity of teleported state with the initial state (in short, the fidelity) of the former is always greater than the fidelity of the latter. In this paper, for Werner's state, we will show that in a range of the related parameter, while the CHSH inequality is violated, the fidelity, which indicates the amount of success of quantum teleportation, is lower than the upper bound of the corresponding fidelity for states that can be simulated with a local hidden variable theory. Meanwhile, we will see that for Gisin's state with hidden nonlocality, filtering, which leads to the appearance of nonlocality and more specifically leads to the violation of the CHSH inequality, also increases the fidelity.

Abstract Background Depending on the classification system used, 5–40% of manic subjects present with concomitant depressive symptoms. This post-hoc analysis evaluates the hypothesis that (hypo)manic subjects have a higher burden of depression than non-(hypo)manic subjects. Methods Data from 806 Bipolar I or II participants of the Stanley Foundation Bipolar Network (SFBN) were analyzed, comprising 17,937 visits. A split data approach was used to separate evaluation and verification in independent samples. For verification of our hypotheses, we compared mean IDS-C scores ratings of non-manic, hypomanic and manic patients. Data were stored on an SQL-server and extracted using standard SQL functions. Linear correlation coefficients and pivotal tables were used to characterize patient groups. Results Mean age of participants was 40 ± 12 years (range 18–81). 460 patients (57.1%) were female and 624 were diagnosed as having bipolar I disorder (77.4%) and 182 with bipolar II (22.6%). Data of 17,937 visits were available for analyses, split into odd and even patient numbers and stratified into three groups by YMRS-scores: not manic

The are substantial studies on distinguishabilities, especially local distinguishability, of quantum states. It is shown that a necessary condition of a local distinguishable state set is the total Schmidt rank not larger than the system dimension. However, if we view states in a larger system, the restriction will be invalid. Hence, a nature problem is that can indistinguishable states become distinguishable by viewing them in a larger system without employing extra resources. In this paper, we consider this problem for (perfect or unambiguous) LOCC1, PPT and SEP distinguishabilities. We demonstrate that if a set of states is indistinguishable in ⊗ k = 1 K C d k , then it is indistinguishable even being viewed in ⊗ k = 1 K C d k + h k , where K , d k ⩾ 2 , h k ⩾ 0 are integers. This shows that such distinguishabilities are properties of states themselves and independent of the dimension of quantum system. Our result gives the maximal numbers of LOCC1 distinguishable states and can be employed to construct a LOCC indistinguishable product basis in general systems. Our result is suitable for general states in general systems. For further discussions, we define the local-global indistinguishable property and present a conjecture. [ABSTRACT FROM AUTHOR]

Background: Depending on the classification system used, 5–40% of manic subjects present with concomitant depressive symptoms. This post-hoc analysis evaluates the hypothesis that (hypo)manic subjects have a higher burden of depression than non-(hypo)manic subjects. Methods: Data from 806 Bipolar I or II participants of the Stanley Foundation Bipolar Network (SFBN) were analyzed, comprising 17,937 visits. A split data approach was used to separate evaluation and verification in independent samples. For verification of our hypotheses, we compared mean IDS-C scores ratings of non-manic, hypomanic and manic patients. Data were stored on an SQL-server and extracted using standard SQL functions. Linear correlation coefficients and pivotal tables were used to characterize patient groups. Results: Mean age of participants was 40 ± 12 years (range 18–81). 460 patients (57.1%) were female and 624 were diagnosed as having bipolar I disorder (77.4%) and 182 with bipolar II (22.6%). Data of 17,937 visits were available for analyses, split into odd and even patient numbers and stratified into three groups by YMRS-scores: not manic < 12, hypomanic < 21, manic < 30. Average IDS-C sum scores in manic or hypomanic states were significantly higher (p <.001) than for non-manic states. (Hypo)manic female patients were likely to show more depressive symptoms than males (p <.001). Similar results were obtained when only the core items of the YMRS or only the number of depressive symptoms were considered. Analyzing the frequency of (hypo)manic mixed states applying a proxy of the DSM-5 mixed features specifier extracted from the IDS-C, we found that almost 50% of the (hypo)manic group visits fulfilled DSM-5 mixed features specifier criteria. Conclusion: Subjects with a higher manic symptom load are also significantly more likely to experience a higher number of depressive symptoms. Mania and depression are not opposing poles of bipolarity but complement each other. [ABSTRACT FROM AUTHOR]

Background and Objectives: Unstable mixed episodes or rapid switching between opposite affective poles within the scope of short cycles was first characterized in 1967 by S. Mentzos as complex polymorphous states with chaotic overlap of manic and depressive symptoms. Well-known examples include antidepressant-induced mania/hypomania and rapid/ultra-rapid/ultradian cycling, when clinicians observe an almost continuous mixed state with a constant change of preponderance of manic or depressive symptoms. Achieving stable remission in these cases is challenging with almost no data on evidence-based treatment. When mood stabilizers are ineffective, electroconvulsive therapy (ECT) has been suggested. Objectives: After reviewing the evidence from available literature, this article presents our own clinical experience of ECT efficacy and tolerability in patients with ultra-rapid cycling bipolar disorder (BD) and unstable mixed states. Materials and Methods: We conducted an open, one-year observational prospective study with a “mirror image” design, including 30 patients with rapid and ultra-rapid cycling BD on long-term mood stabilizer treatment (18 received lithium carbonate, 6 on valproate and 6 on carbamazepine) with limited effectiveness. A bilateral ECT course (5–10 sessions) was prescribed for regaining mood stability. Results: ECT was very effective in 12 patients (40%) with a history of ineffective mood stabilizer treatment who achieved and maintained remission; all of them received lithium except for 1 patient who received carbamazepine and 2 with valproate. Nine patients (30%) showed partial response (one on carbamazepine and two on valproate) and nine patients (30%) had no improvement at all (four on carbamazepine and two on valproate). For the whole sample, the duration of affective episodes was significantly reduced from 36.05 ± 4.32 weeks in the year prior to ECT to 21.74 ± 12.14 weeks in the year post-ECT (p < 0.001). Depressive episodes with mixed and/or catatonic features according to DSM-5 specifiers were associated with a better acute ECT response and/or long-term mood stabilizer treatment outcome after ECT. Conclusions: ECT could be considered as a useful option for getting mood instability under control in rapid and ultra-rapid cycling bipolar patients. Further randomized trials are needed to confirm these results. [ABSTRACT FROM AUTHOR]

Keywords: bipolar; depression; Irritability; mixed states; mood disorders EN bipolar depression Irritability mixed states mood disorders 781 784 4 12/29/20 20201201 NES 201201 It has recently been argued that a unidimensional approach to mood disorders, focusing predominantly on emotions (mood), is too narrow to capture the full spectrum of symptoms of affective disorders, and that additional symptom domains of activity and cognition are at least equally important - possibly even more so.1 This "ACE" (Activity, Cognition and Emotion) model provides more clarity in conceptualising mixed states, the existence of which challenges the predominantly dichotomous view promulgated by DSM and ICD, in which mania and depression are deemed to be mutually exclusive and form two poles of mood disorders with little in between. As irritability is not specific to either mood "pole", and is common in mood disorders, this begs the question - what relationship does irritability have to other symptoms of mood? From the limited findings examining temporal and mechanistic associations between irritability and other mood symptoms, the exact relationship between irritability and mood symptoms is not yet clear (See Table 1). As a transpolar (and transdiagnostic) symptom that appears in both mania and in depression, understanding irritability, and its relationship to other mood symptoms, may help advance our understanding of mood disorders as a whole. [Extracted from the article]

ObjectiveTreatment-resistant depression (TRD) and treatment-resistant bipolar depression (TRBD) poses a significant clinical and societal burden, relying on different operational definitions and treatment approaches. The detection of clinical predictors of resistance is elusive, soliciting clinical subtyping of the depressive episodes, which represents the goal of the present study.MethodsA hundred and thirty-one depressed outpatients underwent psychopathological evaluation using major rating tools, including the Hamilton Rating Scale for Depression, which served for subsequent principal component analysis, followed-up by cluster analysis, with the ultimate goal to fetch different clinical subtypes of depression.ResultsThe cluster analysis identified two clinically interpretable, yet distinctive, groups among 53 bipolar (resistant cases = 15, or 28.3%) and 78 unipolar (resistant cases = 20, or 25.6%) patients. Among the MDD patients, cluster “1” included the following components: “Psychic symptoms, depressed mood, suicide, guilty, insomnia” and “genitourinary, gastrointestinal, weight loss, insight”. Altogether, with broadly defined “mixed features,” this latter cluster correctly predicted treatment outcome in 80.8% cases of MDD. The same “broadly-defined” mixed features of depression (namely, the standard Diagnostic and Statistical Manual for Mental Disorders, Fifth Edition—DSM-5—specifier plus increased energy, psychomotor activity, irritability) correctly classified 71.7% of BD cases, either as TRBD or not.LimitationsSmall sample size and high rate of comorbidity.ConclusionsAlthough relying on different operational criteria and treatment history, TRD and TRBD seem to be consistently predicted by broadly defined mixed features among different clinical subtypes of depression, either unipolar or bipolar cases. If replicated by upcoming studies to encompass also biological and neuropsychological measures, the present study may aid in precision medicine and informed pharmacotherapy.

AbstractBackground.Operational definitions of mania are based on expert consensus rather than empirical data. The aim of this study is to identify the key domains of mania, as well as the relevance of the different signs and symptoms of this clinical construct.Methods.A review of latent factor models studies in manic patients was performed. Before extraction, a harmonization of signs and symptoms of mania and depression was performed in order to reduce the variability between individual studies.Results.We identified 12 studies fulfilling the inclusion criteria and comprising 3039 subjects. Hyperactivity was the clinical item that most likely appeared in the first factor, usually covariating with other core features of mania, such as increased speech, thought disorder, and elevated mood. Depressive–anxious features and irritability–aggressive behavior constituted two other salient dimensions of mania. Altered sleep was frequently an isolated factor, while psychosis appeared related to grandiosity, lack of insight and poor judgment.Conclusions.Our results confirm the multidimensional nature of mania. Hyperactivity, increased speech, and thought disorder appear as core features of the clinical construct. The mood experience could be heterogeneous, depending on the co-occurrence of euphoric (elevated mood) and dysphoric (irritability and depressive mood) emotions of varying intensity. Results are also discussed regarding their relationship with other constitutive elements of bipolar disorder, such as mixed and depressive states.

The debate on mixed states (MS) has been intense for decades. However, several points remain controversial from a nosographic, diagnostic, and therapeutic point of view. The different perspectives that have emerged over the years have turned into a large, but heterogeneous, literature body. The present review aims to summarize the evidence on MS, with a particular focus on mixed depression (MxD), in order to provide a guide for clinicians and encourage the development of future research on the topic. First, we review the history of MS, focusing on their different interpretations and categorizations over the centuries. In this section, we also report alternative models to traditional nosography. Second, we describe the main clinical features of MxD and list the most reliable assessment tools. Finally, we summarize the recommendations provided by the main international guidelines for the treatment of MxD. Our review highlights that the different conceptualizations of MS and MxD, the variability of clinical pictures, and the heterogeneous response to pharmacological treatment make MxD a real challenge for clinicians. Further studies are needed to better characterize the phenotypes of patients with MxD to help clinicians in the management of this delicate condition.

We consider the distillation of quantum coherence in the one-shot setting. The protocol is based on the probabilistic coherence distillation assisted by another party. In this context, coherent states including pure states and mixed states can be transformed into maximally coherent pure state with some probability and the maximal probability is defined as the maximal success probability of assistance. Then we show an upper bound for the maximal success probability of assistance for transforming d-dimensional mixed state to d-dimensional maximally coherent pure state. This upper bound is reached by all mixed states in two- and three-dimensional system and all incoherent states. A lower bound of the maximal success probability of assistance for the full-rank quantum states is also proposed. We also show an upper bound for the maximal success probability of assistance for transforming d-dimensional mixed state to m (m ≤ d) -dimensional maximally coherent pure state in general case. [ABSTRACT FROM AUTHOR]

Objective: Treatment-resistant depression (TRD) and treatment-resistant bipolar depression (TRBD) poses a significant clinical and societal burden, relying on different operational definitions and treatment approaches. The detection of clinical predictors of resistance is elusive, soliciting clinical subtyping of the depressive episodes, which represents the goal of the present study. Methods: A hundred and thirty-one depressed outpatients underwent psychopathological evaluation using major rating tools, including the Hamilton Rating Scale for Depression, which served for subsequent principal component analysis, followed-up by cluster analysis, with the ultimate goal to fetch different clinical subtypes of depression. Results: The cluster analysis identified two clinically interpretable, yet distinctive, groups among 53 bipolar (resistant cases = 15, or 28.3%) and 78 unipolar (resistant cases = 20, or 25.6%) patients. Among the MDD patients, cluster "1" included the following components: "Psychic symptoms, depressed mood, suicide, guilty, insomnia" and "genitourinary, gastrointestinal, weight loss, insight". Altogether, with broadly defined "mixed features," this latter cluster correctly predicted treatment outcome in 80.8% cases of MDD. The same "broadly-defined" mixed features of depression (namely, the standard Diagnostic and Statistical Manual for Mental Disorders, Fifth Edition—DSM-5—specifier plus increased energy, psychomotor activity, irritability) correctly classified 71.7% of BD cases, either as TRBD or not. Limitations: Small sample size and high rate of comorbidity. Conclusions: Although relying on different operational criteria and treatment history, TRD and TRBD seem to be consistently predicted by broadly defined mixed features among different clinical subtypes of depression, either unipolar or bipolar cases. If replicated by upcoming studies to encompass also biological and neuropsychological measures, the present study may aid in precision medicine and informed pharmacotherapy. [ABSTRACT FROM AUTHOR]

Abstract Background Few actigraphy studies in mood disorders have simultaneously included unipolar (UP) and bipolar (BD) depression or BD mixed states as a separate subgroup from mania. This study compared objectively measured activity in UP, BD depression, mania and mixed states and examined if patterns differed according to time of day and/or diagnostic group. Methods Eighty -eight acutely admitted inpatients with mood disorders (52 UP; 18 mania; 12 BD depression; 6 mixed states) underwent 24 hours of actigraphy monitoring. Non-parametric analyses were used to compare median activity level over 24 h (counts per minute), two time series (64-min periods of continuous motor activity) in the morning and evening, and variability in activity across and within groups. Results There was no between-group difference in 24-h median level of activity, but significant differences emerged between BD depression compared to mania in the active morning period, and between UP and mania and mixed states in the active evening period. Within-group analyses revealed that UP cases showed several significant changes between morning and evening activity, with fewer changes in the BD groups. Conclusions Mean activity over 24 hours has limited utility in differentiating UP and BD. In contrast, analysis of non-linear variability measures of activity at different times of day could help objectively distinguish between mood disorder subgroups. Trial registration ClinicalTrials.gov Identifier: NCT01415323 , first registration July 6, 2011.

Background and Objectives: Unstable mixed episodes or rapid switching between opposite affective poles within the scope of short cycles was first characterized in 1967 by S. Mentzos as complex polymorphous states with chaotic overlap of manic and depressive symptoms. Well-known examples include antidepressant-induced mania/hypomania and rapid/ultra-rapid/ultradian cycling, when clinicians observe an almost continuous mixed state with a constant change of preponderance of manic or depressive symptoms. Achieving stable remission in these cases is challenging with almost no data on evidence-based treatment. When mood stabilizers are ineffective, electroconvulsive therapy (ECT) has been suggested. Objectives: After reviewing the evidence from available literature, this article presents our own clinical experience of ECT efficacy and tolerability in patients with ultra-rapid cycling bipolar disorder (BD) and unstable mixed states. Materials and Methods: We conducted an open, one-year observational prospective study with a “mirror image” design, including 30 patients with rapid and ultra-rapid cycling BD on long-term mood stabilizer treatment (18 received lithium carbonate, 6 on valproate and 6 on carbamazepine) with limited effectiveness. A bilateral ECT course (5–10 sessions) was prescribed for regaining mood stability. Results: ECT was very effective in 12 patients (40%) with a history of ineffective mood stabilizer treatment who achieved and maintained remission; all of them received lithium except for 1 patient who received carbamazepine and 2 with valproate. Nine patients (30%) showed partial response (one on carbamazepine and two on valproate) and nine patients (30%) had no improvement at all (four on carbamazepine and two on valproate). For the whole sample, the duration of affective episodes was significantly reduced from 36.05 ± 4.32 weeks in the year prior to ECT to 21.74 ± 12.14 weeks in the year post-ECT (p < 0.001). Depressive episodes with mixed and/or catatonic features according to DSM-5 specifiers were associated with a better acute ECT response and/or long-term mood stabilizer treatment outcome after ECT. Conclusions: ECT could be considered as a useful option for getting mood instability under control in rapid and ultra-rapid cycling bipolar patients. Further randomized trials are needed to confirm these results.

Abstract We propose a nonlinear Schrödinger equation in a Hilbert space enlarged with an ancilla such that the partial trace of its solution obeys to the Lindblad equation of an open quantum system. The dynamics involved by this nonlinear Schrödinger equation constitutes then a purification of the Lindblad dynamics. We study the (non adiabatic) geometric phases involved by this purification and show that our theory unifies several definitions of geometric phases for open systems which have been previously proposed. We study the geometry involved by this purification and show that it is a complicated geometric structure related to a higher gauge theory, i.e. a categorical bibundle with a connective structure. [ABSTRACT FROM AUTHOR]

Objectives: The treatment of mood disorders remains sub‐optimal. A major reason for this is our lack of understanding of the underlying pathophysiology of depression and bipolar disorder. A core problem is the lack of specificity of our current diagnoses. This paper discusses the history of this problem and posits a solution in the form of a more sophisticated model. Method: The authors review the notable historical works that laid the foundations of mood disorder nosology; discuss the more recent influences that shaped modern diagnoses; and examine the evidence that mood disorders are characterised by multidimensional and longitudinal symptom profiles. Results: The ACE model considers mood disorders as a combination of symptoms across three domains: Activity, Cognition, and Emotion; that vary over time. This multidimensional and longitudinal perspective is consistent with the prevalence of complex clinical presentations, such as mixed states, and highlights the importance of recurrence in mood disorders. Conclusions: The ACE model encourages researchers to characterise patients from a number of equally important perspectives and, by doing so, add specificity to the treatment of mood disorders. [ABSTRACT FROM AUTHOR]

We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this expression corresponds to the squared Euclidian distance between the mixed state and the pure one in space of eigenvalues of the density matrix. As an example, geometric measure of mixing for spin-1/2 states is calculated. [ABSTRACT FROM AUTHOR]

Objective: This systematic review provided a critical synthesis and a comprehensive overview of guidelines on the treatment of mixed states. Method: The MEDLINE/PubMed and EMBASE databases were systematically searched from inception to March 21st, 2018. International guidelines covering the treatment of mixed episodes, manic/hypomanic, or depressive episodes with mixed features were considered for inclusion. A methodological quality assessment was conducted with the Appraisal of Guidelines for Research and Evaluation‐AGREE II. Results: The final selection yielded six articles. Despite their heterogeneity, all guidelines agreed in interrupting an antidepressant monotherapy or adding mood‐stabilizing medications. Olanzapine seemed to have the best evidence for acute mixed hypo/manic/depressive states and maintenance treatment. Aripiprazole and paliperidone were possible alternatives for acute hypo/manic mixed states. Lurasidone and ziprasidone were useful in acute mixed depression. Valproate was recommended for the prevention of new mixed episodes while lithium and quetiapine in preventing affective episodes of all polarities. Clozapine and electroconvulsive therapy were effective in refractory mixed episodes. The AGREE II overall assessment rate ranged between 42% and 92%, indicating different quality level of included guidelines. Conclusion: The unmet needs for the mixed symptoms treatment were associated with diagnostic issues and limitations of previous research, particularly for maintenance treatment. [ABSTRACT FROM AUTHOR]

Objectives: Although clinically highly relevant, the recognition and treatment of bipolar mixed states has played only an underpart in recent guidelines. This WFSBP guideline has been developed to supply a systematic overview of all scientific evidence pertaining to the acute and longterm treatment of bipolar mixed states in adults. Methods: Material used for these guidelines is based on a systematic literature search using various data bases. Their scientific rigour was categorised into six levels of evidence (A-F), and different grades of recommendation to ensure practicability were assigned. We examined data pertaining to the acute treatment of manic and depressive symptoms in bipolar mixed patients, as well as data pertaining to the prevention of mixed recurrences after an index episode of any type, or recurrence of any type after a mixed index episode. Results: Manic symptoms in bipolar mixed states appeared responsive to treatment with several atypical antipsychotics, the best evidence resting with olanzapine. For depressive symptoms, addition of ziprasidone to treatment as usual may be beneficial; however, the evidence base is much more limited than for the treatment of manic symptoms. Besides olanzapine and quetiapine, valproate and lithium should also be considered for recurrence prevention. Limitations: The concept of mixed states changed over time, and recently became much more comprehensive with the release of DSM-5. As a consequence, studies in bipolar mixed patients targeted slightly different bipolar subpopulations. In addition, trial designs in acute and maintenance treatment also advanced in recent years in response to regulatory demands. Conclusions: Current treatment recommendations are still based on limited evidence, and there is a clear demand for confirmative studies adopting the DSM-5 specifier with mixed features concept. [ABSTRACT FROM AUTHOR]

Background: Despite the large number of treatments available for bipolar disorder (BD), more than one half of patients have a recurrence within 2 years, and over 90% experience at least one additional affective episode during their lifetime.Methods: The aim of this study was to test the impact of a number of demographic and clinical features on the risk to recurrence in a real- word representative sample of 266 outpatients with BD-I or II treated in a naturalistic setting during a 4-years-follow-up period.Results: We found that the number of episodes per year after study entry, compared to the number of episodes per year before study entry,significantly decreased and that about one third of patients had no recurrences during the observation period. The length of follow-up and the number of previous episodes, mainly depressive, predicted the risk of recurrence, while female gender, higher age at intake, and a higher frequency of past mixed episodes predicted a higher frequency of recurrences.Limitations: The study had some limitations to consider: i.e. the risk of poor reliability of information on the previous course of illness or the naturalistic treatment during the follow-up.Conclusions: Our study suggests that (a) an evidence-based long-term treatment, with regular follow-up visits could improve the course of disease and prognosis; (b) clinicians should carefully consider the presence of a high number of mixed episodes, to provide more targeted treatment strategies; (c) an appropriate use of antidepressants in selected patients did not worsen the course of illness. [ABSTRACT FROM AUTHOR]

Background: Few actigraphy studies in mood disorders have simultaneously included unipolar (UP) and bipolar (BD) depression or BD mixed states as a separate subgroup from mania. This study compared objectively measured activity in UP, BD depression, mania and mixed states and examined if patterns differed according to time of day and/or diagnostic group. Methods: Eighty-eight acutely admitted inpatients with mood disorders (52 UP; 18 mania; 12 BD depression; 6 mixed states) underwent 24 hours of actigraphy monitoring. Non-parametric analyses were used to compare median activity level over 24 h (counts per minute), two time series (64-min periods of continuous motor activity) in the morning and evening, and variability in activity across and within groups. Results: There was no between-group difference in 24-h median level of activity, but significant differences emerged between BD depression compared to mania in the active morning period, and between UP and mania and mixed states in the active evening period. Within-group analyses revealed that UP cases showed several significant changes between morning and evening activity, with fewer changes in the BD groups. Conclusions: Mean activity over 24 hours has limited utility in differentiating UP and BD. In contrast, analysis of non-linear variability measures of activity at different times of day could help objectively distinguish between mood disorder subgroups. [ABSTRACT FROM AUTHOR]