Axioms and Decidability for Type Isomorphism in the Presence of Sums

We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about polynomials with exponentiation that have not been used in our context, we derive: that the usual finite axiomatization known as High-School Identities (HSI) is complete for a significant subclass of types; that it is decidable for that subclass when two types are isomorphic; that, for the whole of the set of types, a recursive extension of the axioms of HSI exists that is complete; and that, for the whole of the set of types, the question as to whether two types are isomorphic is decidable when base types are to be interpreted as finite sets. We also point out certain related open problems

Perspectives for proof unwinding by programming languages techniques

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific essay, written for the audience of proof theorists as well as the working mathematician, is not a survey of the field, but rather a personal view of the author who hopes that it may inspire future and fellow researchers

An interpretation of the Sigma-2 fragment of classical Analysis in System T

We show that it is possible to define a realizability interpretation for the $\Sigma_2$-fragment of classical Analysis using G\"odel's System T only. This supplements a previous result of Schwichtenberg regarding bar recursion at types 0 and 1 by showing how to avoid using bar recursion altogether. Our result is proved via a conservative extension of System T with an operator for composable continuations from the theory of programming languages due to Danvy and Filinski. The fragment of Analysis is therefore essentially constructive, even in presence of the full Axiom of Choice schema: Weak Church's Rule holds of it in spite of the fact that it is strong enough to refute the formal arithmetical version of Church's Thesis

A Direct Version of Veldman's Proof of Open Induction on Cantor Space via Delimited Control Operators

First, we reconstruct Wim Veldman's result that Open Induction on Cantor space can be derived from Double-negation Shift and Markov's Principle. In doing this, we notice that one has to use a countable choice axiom in the proof and that Markov's Principle is replaceable by slightly strengthening the Double-negation Shift schema. We show that this strengthened version of Double-negation Shift can nonetheless be derived in a constructive intermediate logic based on delimited control operators, extended with axioms for higher-type Heyting Arithmetic. We formalize the argument and thus obtain a proof term that directly derives Open Induction on Cantor space by the shift and reset delimited control operators of Danvy and Filinski

Levatiracetam for the management of Lance-Adams syndrome

How to Cite This Article: Ilik F, Ilik MK, Çöven I. Levatiracetam for the management of Lance-Adams syndrome. Iran J Child Neurol. 2014 Spring 8(2):57-59. Chronic post-hypoxic myoclonus, also known as Lance-Adams syndrome (LAS) is a neurological complication characterized by uncontrolled myoclonic jerks following cardiac arrest. In this article, clinical manifestation and symptomatic treatment options are discussed especially concerning the rationale of use of levatiracetam in patients with Lance-Adams syndrome. Clinical presentation is action myoclonus associated with cerebellar ataxia, postural imbalance, and very mild intellectual deficit.An 18-year-old female patient was admitted to our intensive care unit in a coma. She had a cardiorespiratory arrest after a splenectomy in a local hospital. Then, myoclonic movements were continuously observed over the entire body, including the face.On day 14 of hospitalization, we started levatiracetam 1000 mg daily. The frequency of convulsion movements was reduced. The patient level of consciousness was 15 on the Glasgow coma scale (GCS) on the Mini-Mental State Examination (MMSE) score was 23 out of 30. She was later transferred to the rehabilitation department.Vigilance is required to ensure early diagnosis and timely intervention for the myoclonic jerks. In conclusion, we would like to emphasize that LAS should be considered in patients with the myoclonic jerks following cardiac arrest and that levatiracetam therapy may be useful as treatment.References1. Lance JW, Adams RD. The syndrome of intention or action myoclonus as a sequel to hypoxic encephalopathy. Brain 1963; 86: 111-136.2. Guo XH, Yu SY, Liu J, Wu WP, Pu CQ, Zhu K. Posthypoxic myoclonus treated with 5-hydroxytryptophan: a case report. J Clin Neurol 2002; 15: 313-6.3. Arpesella R, Dallocchio C, Arbasino C, Imberti R, Martinotti R, Frucht SJ. A patient with intractable posthypoxic myoclonus (Lance-Adams syndrome) treated with sodium oxybate. Anaesth Intensive Care 2009; 37:314-8.4. Werhahn KJ, Brown P, Rompson PD, Marsden CD. The clinical features and prognosis of chronic post-hypoxic myoclonus. Mov Disord 1997; 12: 216-20.5. Frucht SJ, Trost M, Ma Y, Eidelberg D. The metabolic topography of post-hypoxic myoclonus. Neurology 2004; 62: 1879-1881.6. Frucht S, Fahn S. The clinical spectrum of post-hypoxic myoclonus. Mov Disord 2000; 15 (Suppl 1): 2-7.7. Matsumoto RR, Truong DD, Nguyen KD, Dang AT, Hoang TT, Vo PQ, Sandroni P. Involvement of GABA(A) receptors in myoclonus. Mov Disord 2000; 15(Suppl1):47-52

FLASH: ultra-fast protocol to identify RNA-protein interactions in cells

Determination of the in vivo binding sites of RNA-binding proteins (RBPs) is paramount to understanding their function and how they affect different aspects of gene regulation. With hundreds of RNA-binding proteins identified in human cells, a flexible, high-resolution, high-throughput, highly multiplexible and radioactivity-free method to determine their binding sites has not been described to date. Here we report FLASH (Fast Ligation of RNA after some sort of Affinity Purification for High-throughput Sequencing), which uses a special adapter design and an optimized protocol to determine protein-RNA interactions in living cells. The entire FLASH protocol, starting from cells on plates to a sequencing library, takes 1.5 days. We demonstrate the flexibility, speed and versatility of FLASH by using it to determine RNA targets of both tagged and endogenously expressed proteins under diverse conditions in vivo