François Viète: between analysis and cryptanalysis

François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète’s major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète’s ‘new algebra’ relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète’s algebraic analysis is not an analysis in the same sense as his cryptanalysis is. In Aristotelian terms, the first is a form of ‘’, while the second is a form of . While the first is a top-down argument from the point of view of the human subject, since it is an argument going from what is not actual to what is actual for such a subject, the second one is a bottom-up argument from this same point of view, since it starts from what is first for us and proceed towards what is first by nature.     

Lagrange’s theory of analytical functions and his ideal of purity of method

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline.     

Structural features underlying the selectivity of the kinase inhibitors NBC and dNBC: role of a nitro group that discriminates between CK2 and DYRK1A

8-hydroxy-4-methyl-9-nitrobenzo(g)chromen-2-one (NBC) has been found to be a fairly potent ATP site-directed inhibitor of protein kinase CK2 (Ki = 0.22 μM). Here, we show that NBC also inhibits PIM kinases, especially PIM1 and PIM3, the latter as potently as CK2. Upon removal of the nitro group, to give 8-hydroxy-4-methyl-benzo(g)chromen-2-one (here referred to as “denitro NBC”, dNBC), the inhibitory power toward CK2 is almost entirely lost (IC₅₀ > 30 μM) whereas that toward PIM1 and PIM3 is maintained; in addition, dNBC is a potent inhibitor of a number of other kinases that are weakly inhibited or unaffected by NBC, with special reference to DYRK1A whose IC₅₀ values with NBC and dNBC are 15 and 0.60 μM, respectively. Therefore, the observation that NBC, unlike dNBC, is a potent inducer of apoptosis is consistent with the notion that this effect is mediated by inhibition of endogenous CK2. The structural features underlying NBC selectivity have been revealed by inspecting its 3D structure in complex with the catalytic subunit of Z. mays CK2. The crucial role of the nitro group is exerted both through a direct electrostatic interaction with the side chain of Lys68 and, indirectly, by enhancing the acidic dissociation constant of the adjacent hydroxyl group which interacts with a conserved water molecule in the deepest part of the cavity. By contrast, the very same nitro group is deleterious for the binding to the active site of DYRK1A, as disclosed by molecular docking. This provides the rationale for preferential inhibition of DYRK1A by dNBC.     

Emergence of classical trajectories in quantum systems: the cloud chamber problem in the analysis of Mott (1929)

We analyze the paper “The wave mechanics of $\alpha $ -ray tracks” Mott (Proc R Soc Lond A 126:79–84, 1929), published in 1929 by N. F. Mott. In particular, we discuss the theoretical context in which the paper appeared and give a detailed account of the approach used by the author and the main result attained. Moreover, we comment on the relevance of the work not only as far as foundations of Quantum Mechanics are concerned but also as the earliest pioneering contribution in decoherence theory.     

Activation of type-2 cannabinoid receptor inhibits neuroprotective and antiinflammatory actions of glucocorticoid receptor α: when one is better than two

Endocannabinoids (eCBs) and glucocorticoids (GCs) are two distinct classes of signaling lipids that exert both neuroprotective and immunosuppressive effects; however, the possibility of an actual interaction of their receptors [i.e., type-2 cannabinoid (CB₂) and glucocorticoid receptor α (GRα), respectively] remains unexplored. Here, we demonstrate that the concomitant activation of CB₂ and GRα abolishes the neuroprotective effects induced by each receptor on central neurons and on glial cells in animal models of remote cell death. We also show that the ability of eCBs and GCs, used individually, to inhibit tumour necrosis factor-α (TNF-α) and interferon-γ (IFN-γ) production from activated human T lymphocytes is lost when CB₂ and GRα are activated simultaneously. In addition, signal transduction pathways triggered by concomitant activation of both receptors led to increased levels of GRβ, heat-shock proteins-70 and -90, and p-JNK, as well as to reduced levels of p-STAT6. These effects were reversed only by selectively antagonizing CB₂, but not GRα. Overall, our study demonstrates for the first time the existence of a CB₂-driven negative cross-talk between eCB and GC signaling in both rats and humans, thus paving the way to the possible therapeutic exploitation of CB₂ as a new target for chronic inflammatory and neurodegenerative diseases.     

A recurrent 15q13.3 microdeletion syndrome associated with mental retardation and seizures

We report a recurrent microdeletion syndrome causing mental retardation, epilepsy and variable facial and digital dysmorphisms. We describe nine affected individuals, including six probands: two with de novo deletions, two who inherited the deletion from an affected parent and two with unknown inheritance. The proximal breakpoint of the largest deletion is contiguous with breakpoint 3 (BP3) of the Prader-Willi and Angelman syndrome region, extending 3.95 Mb distally to BP5. A smaller 1.5-Mb deletion has a proximal breakpoint within the larger deletion (BP4) and shares the same distal BP5. This recurrent 1.5-Mb deletion contains six genes, including a candidate gene for epilepsy (CHRNA7) that is probably responsible for the observed seizure phenotype. The BP4-BP5 region undergoes frequent inversion, suggesting a possible link between this inversion polymorphism and recurrent deletion. The frequency of these microdeletions in mental retardation cases is approximately 0.3% (6/2,082 tested), a prevalence comparable to that of Williams, Angelman and Prader-Willi syndromes.     

Axonal loss and neuroinflammation caused by peroxisome-deficient oligodendrocytes

Oligodendrocytes myelinate axons for rapid impulse conduction and contribute to normal axonal functions in the central nervous system. In multiple sclerosis, demyelination is caused by autoimmune attacks, but the role of oligodendroglial cells in disease progression and axon degeneration is unclear. Here we show that oligodendrocytes harbor peroxisomes whose function is essential for maintaining white matter tracts throughout adult life. By selectively inactivating the import factor PEX5 in myelinating glia, we generated mutant mice that developed normally, but within several months showed ataxia, tremor and premature death. Absence of functional peroxisomes from oligodendrocytes caused widespread axonal degeneration and progressive subcortical demyelination, but did not interfere with glial survival. Moreover, it caused a strong proinflammatory milieu and, unexpectedly, the infiltration of B and activated CD8+ T cells into brain lesions. We conclude that peroxisomes provide oligodendrocytes with an essential neuroprotective function against axon degeneration and neuroinflammation, which is relevant for human demyelinating diseases.     

Gain-of-function SOS1 mutations cause a distinctive form of Noonan syndrome

Noonan syndrome is a developmental disorder characterized by short stature, facial dysmorphia, congenital heart defects and skeletal anomalies. Increased RAS-mitogen-activated protein kinase (MAPK) signaling due to PTPN11 and KRAS mutations causes 50% of cases of Noonan syndrome. Here, we report that 22 of 129 individuals with Noonan syndrome without PTPN11 or KRAS mutation have missense mutations in SOS1, which encodes a RAS-specific guanine nucleotide exchange factor. SOS1 mutations cluster at codons encoding residues implicated in the maintenance of SOS1 in its autoinhibited form. In addition, ectopic expression of two Noonan syndrome-associated mutants induces enhanced RAS and ERK activation. The phenotype associated with SOS1 defects lies within the Noonan syndrome spectrum but is distinctive, with a high prevalence of ectodermal abnormalities but generally normal development and linear growth. Our findings implicate gain-of-function mutations in a RAS guanine nucleotide exchange factor in disease for the first time and define a new mechanism by which upregulation of the RAS pathway can profoundly change human development.     

Demonstration of temporal cloaking

Recent research has uncovered a remarkable ability to manipulate and control electromagnetic fields to produce effects such as perfect imaging and spatial cloaking. To achieve spatial cloaking, the index of refraction is manipulated to flow light from a probe around an object in such a way that a 'hole' in space is created, and the object remains hidden. Alternatively, it may be desirable to cloak the occurrence of an event over a finite time period, and the idea of temporal cloaking has been proposed in which the dispersion of the material is manipulated in time, producing a 'time hole' in the probe beam to hide the occurrence of the event from the observer. This approach is based on accelerating the front part of a probe light beam and slowing down its rear part to create a well controlled temporal gap--inside which an event occurs--such that the probe beam is not modified in any way by the event. The probe beam is then restored to its original form by the reverse manipulation of the dispersion. Here we present an experimental demonstration of temporal cloaking in an optical fibre-based system by applying concepts from the space-time duality between diffraction and dispersive broadening. We characterize the performance of our temporal cloak by detecting the spectral modification of a probe beam due to an optical interaction and show that the amplitude of the event (at the picosecond timescale) is reduced by more than an order of magnitude when the cloak is turned on. These results are a significant step towards the development of full spatio-temporal cloaking.