Benign overfitting in linear regression.

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider when a perfect fit to training data in linear regression is compatible with accurate prediction. We give a characterization of linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. The characterization is in terms of two notions of the effective rank of the data covariance. It shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size. By studying examples of data covariance properties that this characterization shows are required for benign overfitting, we find an important role for finite-dimensional data: the accuracy of the minimum norm interpolating prediction rule approaches the best possible accuracy for a much narrower range of properties of the data distribution when the data lie in an infinite-dimensional space vs. when the data lie in a finite-dimensional space with dimension that grows faster than the sample size.

Primary neuroendocrine tumor of the pineal gland: a case report.

INTRODUCTION: Primary intracranial neuroendocrine tumors are exceedingly rare, with few cases in the literature. We present a case of a primary neuroendocrine carcinoma of the pineal gland, which is the second that has ever been reported. CASE PRESENTATION: A 53-year-old male patient presented with vomiting, weakness, and headaches. Imaging revealed a lesion in the pineal region, which was surgically resected. This mass was characterized by histology as a neuroendocrine carcinoma, given the presence of neuroendocrine markers and cytokeratin markers with absence of a primary lesion elsewhere on imaging. CONCLUSIONS: There are currently no guidelines on the management of primary intracranial neuroendocrine tumors. In this case, the patient underwent surgical resection and craniospinal radiotherapy. He subsequently received one cycle of chemotherapy with temozolomide, an alkylating agent, but he unfortunately did not tolerate treatment. A multidisciplinary decision was made along with the patient and his family to focus on palliative care. Eighteen months after the initial presentation, disease recurred in the patient's neck. The patient underwent resection to control the metastases, with a plan to follow with radiotherapy and chemotherapy. Unfortunately, the patient became unwell and died at 21 months after initial diagnosis. This demonstrates a need for continued research and reporting on this uncommon disease entity.

The UK Government should withdraw from the Convention on the Rights of Persons with Disabilities.

SUMMARY: Many psychiatrists in the UK may be surprised to find that the Government ratified a convention ten years ago that suggests compulsory mental health treatment be prohibited. The Convention on the Rights of Persons with Disabilities is arguably the most important legal instrument that no one in psychiatry ever discusses, but if moved from ratification to enforcement it would have enormous effect on day-to-day practice. Here, Dr Paul Gosney argues that the convention if enforced would be damaging for the people it aims to protect, whereas Professor Peter Bartlett defends it as a necessary challenge to the inequalities in our current system.

National survey and analysis of barriers to the utilisation of the 2005 mental capacity act by people with bipolar disorder in England and Wales.

Background: The Mental Capacity Act (2005) (MCA) provides a legal framework for advance planning for both health and welfare in England and Wales for people if they lose mental capacity, for example, through mania or severe depression.Aims: To determine the proportion of people with bipolar disorder (BD) who utilise advance planning, their experience of using it and barriers to its implementation.Methods: National survey of people with clinical diagnosis of BD of their knowledge, use and experience of the MCA. Thematically analysed qualitative interviews with maximum variance sample of people with BD.Results: A total of 544 respondents with BD participated in the survey; 18 in the qualitative study. 403 (74.1%) believed making plans about their personal welfare if they lost capacity to be very important. A total of 199 (36.6%) participants knew about the MCA. A total 54 (10%), 62 (11%) and 21 (4%) participants made advanced decisions to refuse treatment, advance statements and lasting power of attorney, respectively. Barriers included not understanding its different forms, unrealistic expectations and advance plans ignored by services.Conclusion: In BD, the demand for advance plans about welfare with loss of capacity was high, but utilisation of the MCA was low with barriers at service user, clinician and organisation levels.

Gradient Descent with Identity Initialization Efficiently Learns Positive-Definite Linear Transformations by Deep Residual Networks.

We analyze algorithms for approximating a function f(x)=Φx mapping ℜd to ℜd using deep linear neural networks, that is, that learn a function h parameterized by matrices Θ1,…,ΘL and defined by h(x)=ΘLΘL-1…Θ1x . We focus on algorithms that learn through gradient descent on the population quadratic loss in the case that the distribution over the inputs is isotropic. We provide polynomial bounds on the number of iterations for gradient descent to approximate the least-squares matrix Φ , in the case where the initial hypothesis Θ1=…=ΘL=I has excess loss bounded by a small enough constant. We also show that gradient descent fails to converge for Φ whose distance from the identity is a larger constant, and we show that some forms of regularization toward the identity in each layer do not help. If Φ is symmetric positive definite, we show that an algorithm that initializes Θi=I learns an ε -approximation of f using a number of updates polynomial in L , the condition number of Φ , and log(d/ε) . In contrast, we show that if the least-squares matrix Φ is symmetric and has a negative eigenvalue, then all members of a class of algorithms that perform gradient descent with identity initialization, and optionally regularize toward the identity in each layer, fail to converge. We analyze an algorithm for the case that Φ satisfies u⊤Φu>0 for all u but may not be symmetric. This algorithm uses two regularizers: one that maintains the invariant u⊤ΘLΘL-1…Θ1u>0 for all u and the other that "balances" Θ1,…,ΘL so that they have the same singular values.

Identity, law, policy and Communicating Mental Health.

This paper reflects on the special edition, Communicating Mental Health, from the perspective of a legal academic with an interest in the service user rights and in United Nations Convention on the Rights of Persons with Disabilities. It is argued that the special edition demonstrates the breadth of the medical model but also that the medical model remains firmly in place in academic understanding of mental disability. The paper questions what this means for identity formation of people with lived experience of mental disability and how we should conceptualise mental disability in the future.

Litigation Friends or Foes? Representation of 'P' before the Court of Protection.

This article argues that, properly analysed, the common law and the European Convention on Human Rights (ECHR) march hand in hand with the provisions of the Mental Capacity Act 2005 (MCA 2005) so as to impose a set of requirements on litigation friends acting for the subject of applications of proceedings before the Court of Protection ('P') which are very different to those currently understood by practitioners and the judiciary. The authors examine critically current practice and procedures and provide a set of proposals for reforms.

Many were named, but few are current: The Hebeloma of Hesler, Smith, and coauthors.

During the 1970s and 1980s, L. R. Hesler and A. H. Smith, alone, together, or Smith with other authors such as V. S. Evenson and D. H. Mitchel, described numerous North American taxa in Hebeloma. With the inclusion of an early work by Smith and a later work by E. Grilli, who described a species based on material from Smith, 130 taxa were described and form the subject of this paper. Apart from two taxa that were (deliberately) invalidly published and two that were illegitimately published, all others are valid and legitimate names. After study of morphology, habitat, and location of collection (based on available material and information) as well as molecular analysis (insofar as this was successful), of these 128 validly published taxa we regard 14 as being current names; the remaining 114 are synonymized with other current names. These 14 species are Hebeloma albomarginatum, H. alpinicola, H. angelesiense, H. caulocystidiosum, H. immutabile, H. incarnatulum, H. kelloggense, H. mackinawense, H. nitidum, H. olympianum, H. parcivelum, H. praeolidum, H. pungens, and H. sporadicum. This brings up the number of currently recognized, validly published, Hebeloma species in America to 72.

Old but not obsolete: A new life for some of Murrill's (Hebeloma) names.

William Alphonso Murrill was an American mycologist of the early 20th century. He described 1453 new species of Agaricales, Boletales, and Polyporales. Within these were 44 taxa that he described as Hebeloma or that he recombined into Hebeloma. Additionally, there are five species, of which we are aware, that Murrill described within other genera that should be referred to the genus Hebeloma. A further three species described from northern America by J. P. F. C. Montagne, and transferred to Hebeloma by Saccardo, were commented on by Murrill and not accepted within the genus. These 52 taxa are analyzed here, both morphologically and molecularly, as far as possible. For 18 of his types, internal transcribed spacer (ITS) sequences were generated. For two species (H. harperi and H. subfastibile), which were mixed collections, lectotypes are designated. Twenty-three of the taxa analyzed are Hebeloma, as the genus is recognized today, and six of these (H. australe, H. harperi, H. paludicola, H. subaustrale, H. subfastibile, and H. viscidissimum) are regarded as current, i.e., they are names that should be accepted and used. Hebeloma paludicola is an earlier name for H. hygrophilum, described from Europe. Gymnopilus viscidissimus is synonymous with H. amarellum but has priority and is here recombined into Hebeloma. The remaining 17 Hebeloma taxa are synonymized with other species that have priority. The remaining 29 species belong to a range of genera; molecularly supported were Agrocybe, Cortinarius, Inocybe, Inosperma, Phlegmacium, Pholiota, Pseudosperma, and Pyrrhulomyces. Recombinations and synonymizations are made as appropriate and necessary. The names H. alachuanum and H. vatricosum, respectively Inocybe vatricosa, are considered doubtful and should be avoided.

'Appropriate' medical treatment: what's in a word?

Following the amendments in the 2007 Act, there were several revisions made focusing largely on community treatment orders and deprivation of liberty of persons lacking capacity. One of the amendments included a requirement that 'appropriate treatment' be 'available' for compulsion to be imposed in a variety of contexts, most notably admission for treatment under section 3. The definition of appropriate medical treatment within the Act appears largely circular, and therefore of little assistance. The Code of Practice provides some guidance but does little to add to the statutory language. In terms of jurisprudence, there are three reported cases concerning the provision. These cases are analysed and their significance is discussed in an attempt to formulate a clearer definition for appropriate medical treatment.

Species determination using AI machine-learning algorithms: Hebeloma as a case study.

The genus Hebeloma is renowned as difficult when it comes to species determination. Historically, many dichotomous keys have been published and used with varying success rate. Over the last 20 years the authors have built a database of Hebeloma collections containing not only metadata but also parametrized morphological descriptions, where for about a third of the cases micromorphological characters have been analysed and are included, as well as DNA sequences for almost every collection. The database now has about 9000 collections including nearly every type collection worldwide and represents over 120 different taxa. Almost every collection has been analysed and identified to species using a combination of the available molecular and morphological data in addition to locality and habitat information. Based on these data an Artificial Intelligence (AI) machine-learning species identifier has been developed that takes as input locality data and a small number of the morphological parameters. Using a random test set of more than 600 collections from the database, not utilized within the set of collections used to train the identifier, the species identifier was able to identify 77% correctly with its highest probabilistic match, 96% within its three most likely determinations and over 99% of collections within its five most likely determinations.

96 North American taxa sorted - Peck's Hebeloma revisited.

Charles Horton Peck described some 2700 species of North American fungi in the 19th and early 20th centuries. Among these were 31 species that he described as Hebeloma or that later authors recombined into Hebeloma. These 31 taxa have been analyzed morphologically and molecularly, as far as possible. For six of these species, lectotypes are designated. For twelve species, ITS sequences (some partial) were generated. Thirteen of the species analyzed are Hebeloma, as the genus is delimited today. Of these 13, nine are regarded as 'current', i.e. are names that should be accepted and used. Of the remaining four, three are synonymized with earlier Peck species and one with the generic type H. mesophaeum. Numerous Hebeloma species described from America are synonymized with some of Peck's species, such as H. albidulum, H. album, H. colvinii, H. excedens, H. palustre, H. sordidulum, and H. velatum; Peck's H. album, H. palustre, and H. velatum are earlier names for H. fragilipes, H. clavulipes, and H. dunense, respectively. All three names were in current use and described from Europe. The 18 species that are not Hebeloma belong to a range of genera: Agrocybe, Hemistropharia, Inocybe, Inosperma, Naucoria, and Pholiota; three species that were not previously recombined into their respective genera are here recombined and one species, Hebeloma commune is synonymized with Pholiota lenta. Two taxa, that are not Hebeloma, remain unresolved. Sixty later Hebeloma taxa described from North America are revised and synonymized with Peck species and seven with H. mesophaeum, 36 of these supported by ITS (some partial) sequence data. Updates on two species, H. petrakii and H. remyi, from Europe, are also given, and a lectotype and epitype selected for the latter.

Demystifying Hebeloma: introducing hebeloma.org and its database.

We here announce the launch of the website https://hebeloma.org .

Not (only) poison pies - Hebeloma (Agaricales, Hymenogastraceae) in Mexico.

The species of Hebeloma have been little studied in Mexico, but have received attention as edibles and in trials to enhance production of edible fungi and tree growth through inoculation of seedlings with ectomycorrhizal fungi. Here we describe three new species of Hebeloma that are currently known only from Mexico. These species belong to separate sections of the genus: H.ambustiterranum is a member of H.sect.Hebeloma, H.cohaerens belongs to H.sect.Theobromina, while H.magnicystidiatum belongs to H.sect.Denudata. All three species were collected from subtropical pine-oak woodland; all records of H.cohaerens came from altitudes above 2500 m. Hebelomaambustiterranum is commonly sold in the local markets of Tlaxcala as a prized edible mushroom. An additional nine species are reported from Mexico, of which eight are new records for the country: H.aanenii, H.eburneum, H.excedens, H.ingratum, H.neurophyllum, H.sordidulum, H.subaustrale and H.velutipes. First modern descriptions of H.neurophyllum and H.subaustrale, originally described from the USA, are given here.

'The necessity must be convincingly shown to exist': standards for compulsory treatment for mental disorder under the Mental Health Act 1983.

Current English law has few controls on the involuntary treatment of persons detained under the Mental Health Act 1983. In 2001, R (Wilkinson) v. Broadmoor Special Hospital Authority provided some hope that, in conjunction with the Human Rights Act and the European Convention on Human Rights (ECHR), meaningful substantive and procedural standards for compulsory psychiatric treatment might be developed, but that hope has not been fulfilled. Using Wilkinson and the ECHR jurisprudence as a starting point, this article considers when, if at all, compulsory psychiatric treatment might be justified. In particular, it considers the difference between the 'appropriateness' standard of the English legislation and the ECHR requirement of 'therapeutic necessity', the requirements for appropriate procedure and appropriate legislative clarity, how the courts should deal with disagreements among treating physicians, and the relevance of the capacity and best interests of the detained person.

At the Interface Between Paradigms: English Mental Capacity Law and the CRPD.

The United Nations Convention on the Rights of Persons with Disabilities (CRPD) is rightly seen as a break from the past in mental capacity law. At the same time, implementation will occur in the specific existing legal and administrative contexts of each State. This article uses English mental capacity law to explore these issues. The English Mental Capacity Act 2005 (MCA) can be considered the best of the "old" paradigm. The article argues that there are continuities between it and a CRPD-compliant approach. These continuities should be built upon. Further, the implementation of the MCA is still in recent memory. The lessons of that implementation will have considerable application to moves toward CRPD compliance. CRPD compliance is not just about specialist stator guardianship régimes. It is also about a myriad of law, currently capacity based, located in specific legal areas such as contract, wills and succession, and criminal law. Reform in these areas will involve not just disability law, but successful integration into those other legal areas, a matter requiring the involvement of those knowledgeable in those other areas. Since change in these areas will involve the removal of disability as a gateway criterion, they will affect the public as a whole, and the thus, determination of the degree and sort of intervention that the broader public will consider appropriate.

Corrigendum: The Forensic Restrictiveness Questionnaire: Development, Validation, and Revision.

[This corrects the article DOI: 10.3389/fpsyt.2019.00805.].

Perceptions of Restrictiveness in Forensic Mental Health: Do Demographic, Clinical, and Legal Characteristics Matter?

Where safe, forensic mental health systems should provide care in the least restrictive environment possible. Doing so can maximize patient autonomy and empowerment while minimizing unnecessary social disconnection and stigmatization. This study investigated whether patients' perceptions of restrictiveness were associated with demographic, clinical, and legal characteristics. The Forensic Restrictiveness Questionnaire (FRQ) was used to measure perceptions of restrictiveness in 235 patients in low-, medium-, and high-secure settings in England. The results showed that restrictiveness scores were significantly higher for patients who experienced an adverse event in the past week or were diagnosed with a personality disorder compared to those with a mental illness. A regression analysis suggested that only diagnosis was predictive of FRQ scores when controlling for perceptions of ward atmosphere and quality of life. Age, length of stay, ethnicity, level of security, legal section, and offence type were not associated with FRQ scores. Future research should investigate the roles that individual symptoms, insight into illness, mood, personality, and expectations of care have in influencing perceptions of restrictiveness.

Articulating future directions of law reform for compulsory mental health admission and treatment in Hong Kong.

This article explores and outlines four possible pathways for law reform in the area of compulsory mental health admission and treatment in Hong Kong: the (i) abolition, (ii) risk of harm, (iii) mental capacity and (iv) consensus pathways. The discussion of each pathway takes into account local challenges in implementation, as well as Hong Kong's international commitments for the protection of rights. In outlining these pathways for reform, the authors intend to also provide a blueprint for regulatory change in other jurisdictions that are in the process of reforming their mental health laws.